a large simple pendulum is 2 m long. the mass at the end is 3 kg.a. what is the period of oscillation?b. the length of the pendulum is doubled to 4 m. what is the period of oscillation?c. the length of the pendulum is shortened back to 2 m, but the mass is doubled to 6 kg.what is the period of oscillation?

Assuming the same impact time and force, a bigger initial momentum for the cart would result in a larger impulse and change in momentum.

Momentum is defined as mass times velocity. it tells about the moment of the body. it is denoted by p and expressed in kg.m/s. mathematically it is written as p = mv. A body having zero velocity or zero mass has zero momentum. its dimensions is [M¹ L¹ T⁻¹]. Momentum is conserved throughout the motion.

According to conservation law of momentum initial momentum is equal to final momentum.

impulse is the force times time which taken by body to change its momentum.

if the initial momentum is larger then impulse will be larger in collision.

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The glass that produces a torque equal in magnitude and opposite in direction to the torque created by the weight of the glass.

When holding a glass in static equilibrium, the nervous system must balance two forces and one torque. The two forces are the weight of the glass (acting downward) and the force applied by the hand (acting upward). The torque is created by the weight of the glass acting on the center of mass of the glass, which produces a torque that tends to rotate the glass around its center of mass. To keep the glass in static equilibrium, the force applied by the hand must be equal in magnitude and opposite in direction to the weight of the glass, and must be applied at a distance from the center of mass of the glass that produces a torque equal in magnitude and opposite in direction to the torque created by the weight of the glass.

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The water speed in each pipe is the same.

To determine the water speed in each pipe, we need to know the flow rate of the water.

We can calculate the flow rate using the equation:
Q = A * V
where Q is the flow rate, A is the cross-sectional area of the pipes, and V is the velocity of the water.

Assuming that the pipes are carrying the same amount of water, we can set the flow rate for each pipe equal to each other:
Q1 = Q2
A1 * V1 = A2 * V2

We know that the diameter of each pipe is 3.3 meters, so we can calculate the cross-sectional area using the formula:

A = π * (d/2)²
where d is the diameter of the pipe.

Plugging in the values, we get:
A = π * (3.3/2)² = 8.56 m²

So for each pipe, we have:
A1 = A2 = 8.56 m²

Substituting into the flow rate equation, we get:
8.56 * V1 = 8.56 * V2

Dividing both sides by 8.56, we get:
V1 = V2

So the water speed in each pipe is the same. We cannot determine the exact speed without more information, but we know that it is equal in both pipes.

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When Positive charge is distributed uniformly throughout a large insulating cylinder of radius R=0.900 m. The charge per unit length in the cylindrical volume is λ = 3 ×10⁻⁹ C/m. then the magnitude of the electric field at a distance of 0.200 m from the axis of the cylinder is 33.88 N/C.

Electric field is field around electrically charged particle where columbic force of attraction or repulsion can be experienced by other charged particles. It is denoted by letter E and it's SI unit is V/m Volt per meter or N/C newton per coulomb. Electric field comes inward to the center of the negative charge and it is going outward for positive charge.

The electric field E at a point outside the charged cylinder at a distance r is given by,

E = [tex]\frac{\lambda r}{2\epsilon }[/tex]

where λ is charge density, r is distance, ε₀ = 8.854×10⁻¹² m⁻³ kg⁻¹ s⁴A²= permittivity of free space.

Given,

λ =  3 ×10⁻⁹ C/m

radius R = 0.900 m

r = 0.200 m

ε₀ = 8.854×10⁻¹² m⁻³ kg⁻¹ s⁴A².

[tex]E = \frac{\ 3 *10^{-9} *0.2}{2 * 8.854*10^{-12} }[/tex]

E = 33.88 N/C

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When a metal ball is charged by induction using a negatively charged plastic rod, the charge acquired by the metal ball is positive.

This is because the negatively charged plastic rod attracts the positive charges in the metal ball, causing the negative charges to move away from the rod and towards the opposite end of the metal ball.

This leaves the end of the metal ball closest to the rod with a net positive charge, while the far end of the metal ball retains a net negative charge.

This separation of charges results in a positive charge on the end of the metal ball closest to the negatively charged rod.

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To find the speed of nitrogen molecules in the air at the coldest temperature ever recorded in the US, which was -62.1°C (-78.9°F), we can use the formula for root-mean-square (rms) speed of gas molecules:

v_rms = sqrt(3 * R * T / M)

where:
- v_rms is the root-mean-square speed
- R is the universal gas constant (8.314 J/mol·K)
- T is the temperature in Kelvin (convert from Celsius)
- M is the molar mass of nitrogen gas (N₂, approximately 28.0134 g/mol, which needs to be converted to kg/mol)

Step 1: Convert the temperature to Kelvin
T = -62.1°C + 273.15 = 211.05 K

Step 2: Convert the molar mass of nitrogen to kg/mol
M = 28.0134 g/mol * (1 kg/1000 g) = 0.0280134 kg/mol

Step 3: Calculate the rms speed of nitrogen molecules
v_rms = sqrt(3 * 8.314 * 211.05 / 0.0280134) ≈ 509.65 m/s

So, the speed of nitrogen molecules in the air that day was approximately 509.65 m/s.

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Answer: 433.331653

T = -62.1 + 273 = 210.9

MM = 0.0280 = 0.028

V = sqrt((3*8.31*T)/(MM)) = 433.331653

The torque and still get the same change in angular momentum, according to the principle of conservation of angular momentum.  the torque and get the same change in angular momentum Δθ = J / I.

True. The principle of conservation of angular momentum states that the total angular momentum of a system remains constant if no external torque acts on it. This means that if a torque is applied to a system, the system will experience a change in its angular momentum.

The magnitude of the change in angular momentum depends on both the magnitude of the torque and the duration of the torque application. If a larger torque is applied for a shorter time, the change in angular momentum will be the same as if a smaller torque were applied for a longer time.

To see why this is true, we can use the formula for torque:

τ = Iα

where τ is the torque, I is the moment of inertia of the object being rotated, and α is the angular acceleration. Rearranging this equation, we can solve for the angular acceleration:

α = τ / I

Now, if we integrate both sides of the equation with respect to time, we get:

Δθ = ∫(α dt) = ∫(τ / I) dt

where Δθ is the change in angular displacement. If we assume that the moment of inertia of the object remains constant during the torque application, we can take it out of the integral:

Δθ = (1 / I) ∫τ dt

The integral on the right-hand side represents the impulse of the torque, which is equal to the product of the torque and the duration of the torque application:

J = ∫τ dt

Therefore, we can rewrite the equation as:

Δθ = J / I

This equation shows that the change in angular displacement is proportional to the impulse of the torque and inversely proportional to the moment of inertia of the object.

From this equation, we can see that if we increase the duration of the torque application, we can decrease the magnitude of the torque and still get the same change in angular displacement. This is because the product of the torque and the duration of the torque application remains the same, and therefore the impulse of the torque remains constant.

In summary, the magnitude of the change in angular momentum depends on both the magnitude of the torque and the duration of the torque application. If you increase the time over which a torque is applied, you can decrease the magnitude of the torque and still get the same change in angular momentum, according to the principle of conservation of angular momentum.

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The spring balance will register a reading of 588.42 g for the submerged aluminum piece.

To find the reading on the spring balance in grams (g) for the submerged aluminum piece, we need to use the terms density, mass, and buoyancy.

Here's a step-by-step explanation:

1. First, find the volume of the aluminum piece using the formula: Volume = Mass / Density.
  Volume = 775 g / 2.70 g/cm³ = 287.04 cm³

2. Next, calculate the buoyant force exerted on the aluminum by the oil using the formula:

Buoyant Force = Volume × Density of oil × g (acceleration due to gravity)
  Buoyant Force = 287.04 cm³ × 0.650 g/cm³ × 9.81 m/s² = 1830.31 g × m/s²

3. Convert the buoyant force from g × m/s² to grams (g) by dividing by g (9.81 m/s²):
  Buoyant Force (in grams) = 1830.31 g × m/s² / 9.81 m/s² = 186.58 g

4. Finally, find the reading on the spring balance by subtracting the buoyant force from the mass of the aluminum piece:
  Reading on the balance = Mass - Buoyant Force (in grams)
  Reading on the balance = 775 g - 186.58 g = 588.42 g

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a. Fill in the blanks in the following paragraph to identify the properties of mirrors and lenses.

Answer :

Lenses produce images through Refraction, but mirrors produce images through Reflection.

A Concave mirror and a convex lens focus light at a point. A convex mirror and a concave lens spread light apart.

b. Compare the signs of ƒ for lenses and mirrors.

Answer :

ƒ represents the focal length in lenses and mirrors.

For Concave lens and mirror - Value of f is always negative .

For convex lens and mirror - Value of f is always positive .

c. What kind of image is formed when the image distance is positive?

Answer: If the image distance is positive - The image will be formed real and inverted.

What kind of image is formed when the image distance is negative?

Answer: If the image distance is negative - The image will be formed virtual and erect .[tex]~[/tex]

In simple harmonic motion, the magnitude of the acceleration is the greatest when the following conditions apply:
- When the magnitude of the displacement is a maximum
- When the potential energy is a maximum

In simple harmonic motion, the acceleration of an object is directly proportional to its displacement from the equilibrium position and acts towards the equilibrium position. Thus, the magnitude of acceleration is greatest when the displacement is maximum.

This can be seen from the equation of motion for simple harmonic motion: a = -ω^2 x, where a is the acceleration, x is the displacement from the equilibrium position, and ω is the angular frequency of the motion. As the displacement increases, the magnitude of the acceleration also increases.

On the other hand, the speed is maximum and the kinetic energy is minimum at the equilibrium position, where the displacement is zero. The potential energy is maximum at the maximum displacement from the equilibrium position, where the magnitude of the acceleration is also maximum.

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When catching an egg, it's generally better to aim for a larger value of Δt, which represents the time it takes to bring the egg to a stop. This is because the force exerted on the egg is inversely proportional to the time interval Δt, as described by the impulse-momentum theorem:

Impulse = Force × Δt = change in momentum

A larger Δt means that the force exerted on the egg is smaller, making it less likely for the egg to crack or break.

When you catch the egg by gradually slowing it down, you're effectively increasing the time interval Δt, thus reducing the force acting upon the egg.

In contrast, a smaller Δt corresponds to a larger force, which increases the risk of breaking the egg due to a more abrupt stop.

So, to minimize the risk of breaking the egg, it's best to catch it in such a way that Δt is large, allowing for a gentler deceleration and a lower force acting on the egg.

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The voltage across the 2800-Ω resistor is approximately 9.88 V.

To find the voltage across the 2800-Ω resistor when it is connected in series with a 600-Ω resistor and a 12-V battery, follow these steps:

1. Calculate the total resistance (R_total) in the series circuit:
R_total = R1 + R2 = 600 Ω + 2800 Ω = 3400 Ω

2. Calculate the total current (I_total) flowing through the circuit using Ohm's Law:
I_total = Voltage / R_total = 12 V / 3400 Ω ≈ 0.00353 A

3. Calculate the voltage across the 2800-Ω resistor (V2) using Ohm's Law:
V2 = I_total ×R2 = 0.00353 A ×2800 Ω ≈ 9.88 V

The voltage across the 2800-Ω resistor is approximately 9.88 V.

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The absolute temperature changes by a factor of 5.0 when the pressure is five times bigger, with volume and molar quantity held constant.

To determine by what factor the absolute temperature changes for an ideal gas when the pressure is five times bigger, with volume and molar quantity held constant, we will use the ideal gas law equation: PV = nRT.

In this case, since the volume (V) and the molar quantity (n) are constant, we can rearrange the equation to find the relationship between pressure (P) and temperature (T):

P1/T1 = P2/T2

Given that the pressure is five times bigger, P2 = 5 * P1. Now, we'll substitute this into the equation:

P1/T1 = (5 * P1)/T2

Since P1 is present on both sides of the equation, we can cancel it out:

1/T1 = 5/T2

Now, we want to find the factor by which the temperature changes (T2/T1):

T2/T1 = 5

So, when the pressure is five times greater, the absolute temperature changes by a factor of 5.0 but the volume and molar quantity remain constant.

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In fact, some research has suggested that angry speech may actually be characterized by shorter phoneme durations, as well as higher fundamental frequencies and greater variability in pitch and loudness.

The FALSE sentence is B. The duration of phonemes in a person's speech is typically not longer when they are angry.

The fundamental frequency of a person's speech tends to vary based on their emotional state. When a person is excited or joyful, their fundamental frequency tends to be higher, while when they are sad, their fundamental frequency tends to be lower. The duration of phonemes in a person's speech can also vary with their emotional state, but the general pattern is that phonemes are typically longer when a person is happy or relaxed, and shorter when they are stressed or anxious.

However, there is little evidence to suggest that the duration of phonemes in a person's speech is typically longer when they are angry. In fact, some research has suggested that angry speech may actually be characterized by shorter phoneme durations, as well as higher fundamental frequencies and greater variability in pitch and loudness.

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The given statement, "If a body starts with zero velocity and ends with zero velocity, then the area under the positive acceleration curve must be equal to the area under the negative acceleration curve," is True. This is because positive acceleration causes an increase in velocity, while negative acceleration causes a decrease in velocity.

In order for the body to return to zero velocity, the total change in velocity due to positive acceleration must be canceled out by the total change in velocity due to negative acceleration, meaning that the areas under both curves must be equal.

The area under the positive acceleration curve represents the increase in velocity during the displacement, while the area under the negative acceleration curve represents the decrease in velocity during the return to the original position. Since the body ends with zero velocity, the areas under both curves must be equal in magnitude and opposite in sign, resulting in a net area of zero.

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When the block is launched with four times the speed, its kinetic energy will increase by a factor of 16 (4^2) since kinetic energy is proportional to the square of the velocity. Therefore, when it hits the spring, the spring will compress by a factor of 16x (where x is the original amount of compression).

This can be seen from the equation for the potential energy stored in a spring:

U = (1/2)kx^2

where U is the potential energy stored in the spring, k is the spring constant, and x is the amount of compression.

Since the block's kinetic energy is increasing by a factor of 16, the work done by the block on the spring will also increase by a factor of 16. Therefore, we can write:

(1/2)mv^2 = 16(1/2)kx^2

Kinetic energy is the energy an object has because of its motion. If we want to accelerate an object, then we must apply a force. Applying a force requires us to do work. After work has been done, energy has been transferred to the object, and the object will be moving with a new constant speed

Simplifying this equation, we get:

x = (1/4)^(1/2) * x

Therefore, the spring will compress by a factor of 1/2 (or 0.5) of its original amount when the block is launched with four times the speed.

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The mass of the block on the 36.87° incline is 4.00 kg, which corresponds to option 3.

To solve this problem, we need to consider the forces acting on each block and set up an equilibrium condition. Since the blocks are not moving, the forces on both inclines must be equal and opposite.

We can use the formula for gravitational force: F = mg, where F is the force, m is the mass, and g is the acceleration due to gravity (approximately 9.81 m/s²).

For the 6.00 kg block on the 30.0° incline, the force acting perpendicular to the incline is F1 = (6.00 kg)(9.81 m/s²)sin(30.0°).

For the unknown mass block on the 36.87° incline, let its mass be M. The force acting perpendicular to the incline is F2 = (M)(9.81 m/s²)sin(36.87°).

Since the blocks are in equilibrium, F1 = F2.

(6.00 kg)(9.81 m/s²)sin(30.0°) = (M)(9.81 m/s²)sin(36.87°)

Solving for M, we find that M ≈ 4.00 kg. Therefore, the mass of the block on the 36.87° incline is 4.00 kg, which corresponds to option 3.

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The wavelengths of the photons in the universe have been stretched by a factor of approximately 3.66 x 10⁸ since the end of the era of nucleosynthesis.

To compare the peak wavelength of the radiation in the universe at the end of the era of nucleosynthesis with the peak wavelength of the radiation in the universe currently, we will first need to find the peak wavelengths at both times. We will use Wien's Law, which states that the peak wavelength (λ) is inversely proportional to temperature (T): λ = b/T, where b is Wien's constant (2.898 x 10⁻³ m*K).

1. Calculate the peak wavelength at the end of the era of nucleosynthesis:
- Temperature (T1) = 10⁹ K
- λ1 = b/T1 = (2.898 x 10⁻³)/(10⁹) = 2.898 x 10⁻¹² m

2. Calculate the current peak wavelength of radiation in the universe:
- Current temperature (T2) = 2.73 K (cosmic microwave background temperature)
- λ2 = b/T2 = (2.898 x 10⁻³)/(2.73) = 1.061 x 10⁻³m

3. Find the stretching factor by dividing the current peak wavelength by the peak wavelength at the end of nucleosynthesis:
- Stretching factor = λ2/λ1 = (1.061 x 10⁻³)/(2.898 x 10⁻¹²) = 3.66 x 10⁸

So, the wavelengths of the photons in the universe have been stretched by a factor of approximately 3.66 x 10⁸since the end of the era of nucleosynthesis.

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A planet that has one third the mass of Earth and one third the radius of Earth has an escape velocity of  approximately 7.67 km/s.

To calculate the escape velocity of a planet with one third the mass and radius of Earth, we can use the formula for escape velocity:

escape velocity = √(2GM/r)

where G is the gravitational constant, M is the mass of the planet, and r is the radius of the planet.

Since the planet has one third the mass and radius of Earth, we can substitute these values into the formula:

M = (1/3)M_Earth

r = (1/3)r_Earth

where M_Earth and r_Earth are the mass and radius of Earth, respectively.

Substituting these values into the formula for escape velocity, we get:

escape velocity = √(2G(1/3)M_Earth/(1/3)r_Earth)

Simplifying this expression, we get:

escape velocity = √(2GM_Earth/r_Earth)

Therefore, the escape velocity of a planet with one third the mass and radius of Earth is the same as the escape velocity of Earth, which is approximately 11.2 km/s.
Hi! The escape velocity of a planet can be calculated using the formula:

Escape Velocity = √(2 * G * M / R)

where G is the gravitational constant (approximately 6.674 × 10^-11 m³ kg⁻¹ s⁻²), M is the mass of the planet, and R is the radius of the planet.

In this case, the planet has 1/3 the mass (M) and 1/3 the radius (R) of Earth. The mass and radius of Earth are approximately 5.972 × 10^24 kg and 6,371,000 meters, respectively.

So, for this planet:
M = (1/3) * 5.972 × 10^24 kg
R = (1/3) * 6,371,000 meters

Plug these values into the escape velocity formula:

Escape Velocity = √(2 * (6.674 × 10^-11 m³ kg⁻¹ s⁻²) * ((1/3) * 5.972 × 10^24 kg) / ((1/3) * 6,371,000 meters))

After calculating, the escape velocity for this planet is approximately 7.67 km/s.

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Answer:

Weight is the force exerted on an object due to gravity and is calculated as the product of an object’s mass and the acceleration due to gravity. On Earth, the acceleration due to gravity is approximately 9.8 m/s^2. So, if a person weighs 784 N on Earth, their mass would be 784 N / 9.8 m/s^2 = 80 kg.

On the moon, where the acceleration due to gravity is 1.60 m/s^2, this person would weigh 80 kg * 1.60 m/s^2 = 128 N.

Explanation:

The coefficient of static friction between the crate and the surface it is on is 0.362.

The force required to set a stationary crate in motion is given by the product of the coefficient of static friction (μs) and the normal force (N) acting on the crate. Thus, we can use the following formula to find μs:

μs = F / N

where F is the force required to set the crate in motion.

Substituting the given values of F = 275 N and m = 77.3 kg, we can find N using the formula N = mg, where g is the acceleration due to gravity.

N = (77.3 kg)(9.81 m/s²) = 758.413 N

Therefore, the coefficient of static friction is:

μs = F / N = 275 N / 758.413 N = 0.362

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A space hauler and cargo module with a total mass of M travel with initial velocity [tex]v_i[/tex] relative to the Sun. After ejecting the module, the velocity of the hauler relative to the Sun is 1975 km/h.

Let's start by applying the law of conservation of momentum. Assuming that there are no external forces acting on the system, the total momentum before the explosion is equal to the total momentum after the explosion.

Let's denote the mass of the hauler as m₁, the mass of the module as m₂, the initial velocity of the hauler relative to the sun as v₁, and the velocity of the hauler relative to the module as v₂. We know that m₁ + m₂ = M, and that m₂ = 0.20M.

Before the explosion, the total momentum of the system is

P₁ = m₁*v₁

After the explosion, the hauler and the module move in opposite directions. Let's assume that the hauler moves to the right and the module moves to the left. The total momentum of the system after the explosion is

P₂ = m₁*(v₁ + 500 km/h) + m₂*(-v)

where the negative sign in front of v₂ indicates that the module is moving in the opposite direction to the hauler.

By applying the conservation of momentum, we can set P₁ equal to P₂:

m₁v₁ = m₁(v₁ + 500 km/h) + m₂*(-v₂)

Simplifying this equation gives

v₁ = v2/5

Since m₂ = 0.20M and m₁ + m₂ = M, we have m₁ = 0.80M. Therefore:

v₁ = v₂/5 = (-0.20M)/(0.80M) * 500 km/h = -125 km/h

The negative sign indicates that the hauler is moving in the opposite direction to the initial velocity [tex]v_i[/tex]. Therefore, the velocity of the hauler relative to the Sun is

[tex]v_{1final}[/tex] = [tex]v_i[/tex] + v₁ = 2100 km/h - 125 km/h = 1975 km/h

So the velocity of the hauler relative to the Sun is 1975 km/h.

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--The given question is incomplete, the complete question is given

" A space hauler and cargo module, of total mass M, travels along an x axis in deep space. They have an initial velocity vi of magnitude 2100 km/h relative to the Sun. With a small explosion, the hauler ejects the cargo module, of mass 0.20M. The hauler then travels 500 km/h faster than the module along the x axis; that is, the relative speed between the hauler and the module is 500 km/h. What then is the velocity of the hauler relative to the Sun?"--

Eric has a mass of 60 kg. He is standing on a scale in an elevator that is accelerating downward at 1.7 m/[tex]s^{2}[/tex]

Hence, the correct option is C.

The force acting on Eric is the force due to gravity and the force due to the acceleration of the elevator.

The weight of Eric is given by

W = mg

Where W is the weight, m is the mass, and g is the acceleration due to gravity.

W = (60 kg)(9.8 m/[tex]s^{2}[/tex])

W =  588 N

The force due to the acceleration of the elevator is given by

F = ma

Where F is the force, m is the mass, and a is the acceleration of the elevator (-1.7 m/[tex]s^{2}[/tex] since it's accelerating downwards).

F = (60 kg)(-1.7 m/[tex]s^{2}[/tex]) = -102 N

F = -102 N

The approximate reading on the scale is the sum of the weight of Eric and the force due to the acceleration of the elevator.

Reading = W + F = 588 N - 102 N

Reading = = 486 N

Therefore, the approximate reading on the scale is 486 N.

Hence, the correct option is C.

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A test charge is placed successively at points I, II, and III. If edge effects are negligible, the force on the charge when it is at point III is of equal magnitude and in the same direction as the force on the charge when it is at point II. hence option B is correct.

Electric charge is the physical property of matter that experiences force when it is placed in electric field. F = qE where q is amount of charge, E = electric field and F = is force experienced by the charge. there are two types of charges, positive charge and negative charge which are generally carried by proton and electron resp. like charges repel each other and unlike charges attract each other. the flow charges is called as current. Elementary charge is amount of charge a electron is having, whose value is 1.602 x 10⁻¹⁹ C

hence the force F acting on the charge when it is in between two plates is,

F = qE

which do not depends on the distance from the plate inside the plates.

Hence option B is correct.

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The total pressure is approximately 83.47 times greater at a depth of 850 m in water than at the surface.

To determine by what factor the total pressure is greater at a depth of 850 m in water than at the surface where pressure is one atmosphere, we need to follow these steps:

Step 1: Calculate the pressure due to water at 850 m depth
The pressure due to water at a certain depth can be calculated using the formula:
P_water = water density * g * depth

Step 2: Plug in the given values
P_water = (1.0 * 10³ kg/m³) * (9.8 m/s²) * (850 m)

Step 3: Calculate the pressure due to water
P_water = 8,330,000 N/m²

Step 4: Add the atmospheric pressure
Total pressure at 850 m depth = P_water + 1 atmosphere pressure
Total pressure at 850 m depth = 8,330,000 N/m² + 1.01 * 10⁵ N/m²
Total pressure at 850 m depth = 8,431,000 N/m²

Step 5: Calculate the factor by which the pressure is greater at 850 m depth than at the surface
Factor = Total pressure at 850 m depth / Atmospheric pressure at the surface
Factor = 8,431,000 N/m² / 1.01 * 10⁵ N/m²
Factor ≈ 83.47

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If the sphere is placed in water, the maximum iron mass that can be suspended by a string from it so that it does not sink would be 4.85 kg.

To determine the maximum iron mass that can be suspended from the styrofoam sphere without causing it to sink, we need to calculate the buoyant force acting on the sphere.

The buoyant force is equal to the weight of the displaced water, which is determined by the volume of the sphere submerged in water.

First, we need to calculate the volume of the sphere using its diameter:

Volume = [tex](4/3) \times \pi  \times (diameter/2)^3[/tex]
Volume = [tex](4/3) \times \pi  \times (45cm/2)^3[/tex]
Volume = [tex]3.87 \times 10^5 cm^3[/tex]

Next, we need to convert the volume to cubic meters:

Volume = [tex]3.87 \times 10^-1 m^3[/tex]

Since the density of the styrofoam is given as [tex]152 kg/m^3[/tex], we can calculate its mass as:

Mass = density x volume
Mass =[tex]152 kg/m^3 \times 3.87 \times 10^-1 m^3[/tex]
Mass = 58.5 kg

Now, we can calculate the buoyant force acting on the sphere:

Buoyant force = weight of displaced water
Buoyant force = density of water x volume of submerged sphere x acceleration due to gravity
Buoyant force = [tex]1000 kg/m^3 \times (4/3) \times \pi  \times (22.5cm/100)^3 \times 9.81 m/s^2[/tex]
Buoyant force = 47.5 N

Finally, we can calculate the maximum iron mass that can be suspended from the sphere using the buoyant force:

Maximum iron mass = buoyant force/acceleration due to gravity
Maximum iron mass = [tex]47.5 N / 9.81 m/s^2[/tex]
Maximum iron mass = 4.85 kg

Therefore, the maximum iron mass that can be suspended from the styrofoam sphere without causing it to sink is approximately 4.85 kg.

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The mass of the car in terms of the given quantities is: mcar = (1/3) * m1 * (v^2 / vcar^2)

We found the kinetic energy of the flywheel to be:

K = (1/2) * m1 * v^2

If one third of this kinetic energy is transferred to car, then kinetic energy of car can be expressed as:

Kcar = (1/3) * K = (1/3) * (1/2) * m1 * v^2 = (1/6) * m1 * v^2

The kinetic energy of the car can also be expressed in terms of its mass  and speed as:

Kcar = (1/2) * mcar * vcar^2

Setting these two expressions for Kcar equal to each other and solving for mcar, we get:

(1/6) * m1 * v^2 = (1/2) * mcar * vcar^2

mcar = (1/3) * m1 * (v^2 / vcar^2)

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For the two charges with charge +Q placed at opposite corners of the square, the potential at the point p is determined as (2kQ) / d  V.

The electric potential is the work done in bringing the unit positive charge from one point to another. It equals the charge and distance between the charges. The potential is directly proportional to the charges and inversely proportional to the distance of separation of charges.

The potential is defined as,  V = kQ/ r. In a square at a point p, the potential due to charge Q₁ is V₁ = kQ / d (where d is the side length of the square) and due to charge Q₂ is V₂ = kQ / d.  

The net electric potential is,

V = V₁ + V₂

   = (kQ / d) + (kQ / d)

   = 2 (kQ/d)

The potential at a point p in a square is V = 2 (kQ/d) V.

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The period of the pendulum will increase when the elevator is accelerating upward.

The period of a pendulum is the time it takes for one complete oscillation, which is determined by the length of the pendulum and the acceleration due to gravity. In an elevator at rest, the acceleration due to gravity is the only force acting on the pendulum, and its period is T.

However, when the elevator accelerates upward, the effective gravitational force on the pendulum is reduced, causing the period to increase. This is because the pendulum experiences a net force in the upward direction, which reduces the effective acceleration due to gravity.

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