Question

the linear momentum of a body is increased by 10% what is the percentage change in its kinetic energy. explain.

Answer 1

There are two case for change of momentum. First by ((increase in mass and keeping the velocity unchanged, the second by keeping the mass unchanged and changing the velocity.

Case1. Velocity unchanged, mass increases by 10%.

Let the original massif the body = m,

New increased mass 1.1 m

Let the velocity be = v

K. E with original mass = 1/2 m v²

K. E with increased mass = 1/2 × 1.1 m v²

Change in K. E= 1/2 m v² (1.1 - 1) = 0.1 of original K. E =10% change in K. E.

Case2: Mass unchanged velocity increases

Original velocity= v

Original K. E= 1/2 m v²

Changed velocity= 1.1 v

New K. E. = 1/2 m (1.1 v)² = 1.21 of original K. E.

% change in K. E= [(1.21 - 1) of original K. E/ original K. E]×100= 21%