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if the linear momentum of a body is increased by 10% what will be the percentage change in it's kinetic energy

Let m be mass and v be the velocity of particle.

Kinetic energy K = (1/2) m v2 ........................... (1)

Momentum P = m v  ........................(2)

By multiplying kinetic energy by mass m and dividing again by mass m and using eqn.(2) , we get

K = [ P2 / ( 2 m ) ]

By taking logarithm and differentiate above expression, we get

Hence if momentum increased by 10% , then kinetic energy increased by 20%

Answered by Thiyagarajan K | 27 Jan, 2024, 10:10: AM

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