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Two bodies of mass m and 4 m have equal kinetic energy. What is the ratio of their momentum?
When two bodies of masses m and 4m have the same amount of kinetic energy, their momenta differ because the relationship between kinetic energy and momentum is such that kinetic energy depends on both mass and the square of velocity, while momentum depends linearly on mass and velocity. The velocityRead more
When two bodies of masses m and 4m have the same amount of kinetic energy, their momenta differ because the relationship between kinetic energy and momentum is such that kinetic energy depends on both mass and the square of velocity, while momentum depends linearly on mass and velocity.
The velocity of a heavier body will have to be lower than that of a lighter body in order to have the same kinetic energy. For the kinetic energy being constant, the momentum of a body varies directly as the square root of its mass. So when their momenta are compared, the ratio of the momenta is equal to the square root of the ratio of the masses.
In this case, the first body has mass m, while the second has a mass of 4m. The square root of their mass ratio, √1} : √4, gives the momentum ratio as 1:2. This means the body with four times the mass has double the momentum of the lighter body under equal kinetic energy conditions.
Hence, the kinetic energy of both bodies is the same, but their momentum differs because of the mass in these bodies. It is greater in the former body compared with the later.
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A body moving with a velocity v, breaks up into two equal parts. One of the parts retraces back with velocity v, Then the velocity of the other part is
When a body breaks into two equal parts and is moving at some velocity, then its behavior may be analyzed using the principle of conservation of momentum. First, the whole body has some momentum because of the mass and the velocity of that body. The part, while breaking, travels backward with the saRead more
When a body breaks into two equal parts and is moving at some velocity, then its behavior may be analyzed using the principle of conservation of momentum. First, the whole body has some momentum because of the mass and the velocity of that body. The part, while breaking, travels backward with the same speed of the original velocity of the body.
In this case, if one part traces its trajectory with the same speed, we must calculate the velocity of the second part. Since momentum is conserved everywhere, the total momentum before and after the break will be the same.
In that case, one part moving in the opposite direction with the same speed gives a negative contribution to the total momentum of the system. The other portion must make up for this alteration in order to ensure that the sum of the momentums remains unchanged. By the law of conservation of momentum, it is apparent that the second portion has to move in the forward direction at a greater velocity. More precisely, its velocity will be three times the original velocity of the body before it broke up. This shows how motion and the conservation principles are interrelated in physics. Finally, the second part of the body moves with a velocity three times greater than that of the original body.
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The bob of a pendulum of length 2 m lies at P. When it reaches Q, it loses 10 % of its total energy due to air resistance. The velocity at Q is
We first need to understand the system. When the pendulum is at point P, it has maximum potential energy and no kinetic energy because it is momentarily at rest. Now, as the pendulum swings down to point Q, the potential energy gets converted into kinetic energy. To find the velocity of the pendulumRead more
We first need to understand the system. When the pendulum is at point P, it has maximum potential energy and no kinetic energy because it is momentarily at rest. Now, as the pendulum swings down to point Q, the potential energy gets converted into kinetic energy. To find the velocity of the pendulum bob at point Q after losing 10% of its energy due to air resistance, we begin with understanding the system.
However, during this process, the pendulum loses 10% of its total mechanical energy to air resistance. Thus, only 90% of the initial total energy is available for conversion into kinetic energy at point Q. The energy conversion results in the pendulum bob gaining speed as it moves downward.
We can calculate the velocity at point Q. The lost energy is the one that reduces the kinetic energy the bob can have at the lowest point. The remaining energy translates into kinetic energy, which can be expressed in terms of the mass of the bob and its velocity.
Ultimately, taking into consideration the energy transformations and the energy loss effect we observe that the pendulum bob at point Q will have a velocity of 6 meters per second. The answer is, therefore, 6 m/s.
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When a spring is stretched by 2 cm, it stores 100J of energy. If it is stretched further by 2 cm, the stored energy will be increased by
When a spring is stretched, the energy stored in it is given by the formula for elastic potential energy, which is proportional to the square of the displacement from its equilibrium position. If the spring is initially stretched by 2 cm and stores 100 J of energy, stretching it further by another 2Read more
When a spring is stretched, the energy stored in it is given by the formula for elastic potential energy, which is proportional to the square of the displacement from its equilibrium position. If the spring is initially stretched by 2 cm and stores 100 J of energy, stretching it further by another 2 cm results in a total stretch of 4 cm.
The energy stored in the spring at any stretch can be expressed as follows:
1. For the first stretch of 2 cm:
Energy = k ⋅ (2²) = k ⋅ 4 (where k is the spring constant)
2. For the total stretch of 4 cm:
Energy = k ⋅ (4²) = k ⋅ 16
The increase in energy when stretched from 2 cm to 4 cm can be calculated as follows:
– Total energy at 4 cm: k .16
– Initial energy at 2 cm: k . 4
The increase in energy will then be:
– Increase in energy = k . 16 – k . 4 = k . 12
Given that k⋅4 = 100 J, we know that the total energy stored at 4 cm is 4⋅ 100 = 400 J.
Hence, the amount of increase in the energy stored when the spring is stretched further by 2 cm is: 300 J.
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What is the angular momentum of a particle of mass 𝑚 moving with velocity 𝑣 at a perpendicular distance 𝑟 from the axis of rotation?
Angular momentum is given by 𝐿 = 𝑟 × 𝑝 = 𝑟 ⋅ 𝑚 ⋅ 𝑣 ⋅sin 𝜃, where 𝜃 = 90° (perpendicular). Therefore, L=mvr. This question related to Chapter 6 physics Class 11th NCERT. From the Chapter 6 System of Particles and Rotational Motion. Give answer according to your understanding. For more please visit heRead more
Angular momentum is given by 𝐿 = 𝑟 × 𝑝 = 𝑟 ⋅ 𝑚 ⋅ 𝑣 ⋅sin 𝜃, where 𝜃 = 90° (perpendicular). Therefore, L=mvr. This question related to Chapter 6 physics Class 11th NCERT. From the Chapter 6 System of Particles and Rotational Motion. Give answer according to your understanding.
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