Question

two bodies of masses m and 4m moving with equal momentum then find ratio of their kinetic energies ?

Answer 1

HEYA !!
KINETIC ENERGY IS GIven by
K = 1/2 m v²
Multiply and divide by m
We get
K = 1/2 × (mv)²/m
We know linear momentum is given by p = mv
This K = 1/2p²/m

Now for mass m
K = 1/2m × p²

For mass 4m
K' = 1/8m × p²
Now k/k' = 1/2m × p²/1/8m × p²
=> K/K' = 4:1

Answer 2

We know that ,
K = p^2/2m

For mass m
K = p^2/2m

For mass 4m,
K" = p^2/2(4m) = p^2/8m

Ratio, K:K" = p^2/2m x 8m/p^2 = 4 : 1

Hope This Helps You!