Direction: In the following questions, a statement of assertion is fo...
Kinetic energy of a body of mass m
1,
Again, kinetic energy of a body of mass m2,
If

As given m2 > m1
Therefore, K1 > K2 i.e. the kinetic energy of light body will be more than the kinetic energy of heavy body when both have same momentum.
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Direction: In the following questions, a statement of assertion is fo...
Assertion : A light body and heavy body have same momentum. Then they also have the same kinetic energy.
Reason : Kinetic energy depends on the mass of the body.
To answer this question, let's understand the concepts of momentum and kinetic energy.
Momentum:
- Momentum is a property of a moving object and is defined as the product of its mass and velocity.
- Mathematically, momentum (p) can be expressed as p = m * v, where m is the mass of the object and v is its velocity.
- Momentum is a vector quantity, which means it has both magnitude and direction.
Kinetic Energy:
- Kinetic energy is the energy possessed by an object due to its motion.
- It depends on both the mass and the velocity of the object.
- Mathematically, kinetic energy (K.E.) can be expressed as K.E. = (1/2) * m * v^2, where m is the mass of the object and v is its velocity.
Now, let's analyze the given assertion and reason.
Assertion: A light body and heavy body have the same momentum. Then they also have the same kinetic energy.
Reason: Kinetic energy depends on the mass of the body.
From the given reason, we know that kinetic energy depends on the mass of the body. This means that if the mass of two objects is different, their kinetic energies will also be different.
However, the assertion states that a light body and a heavy body have the same momentum. Momentum depends on both mass and velocity. If the momentum of both objects is the same, it means that their masses and velocities are inversely proportional to each other. This implies that the light body will have a higher velocity compared to the heavy body.
Since kinetic energy depends on both mass and velocity, the light body will have a higher kinetic energy than the heavy body. Therefore, the assertion is false because two bodies with the same momentum do not necessarily have the same kinetic energy.
Hence, the correct answer is option 'D' - Assertion is false but the reason is true.