Question

Question #26e1f

Answer 1

We know that KE (`E`) and momentum (`p`) of a body of mass `m` is related as follows

`E =p^2/(2m)`

If `E_i and p_i` are respectively initial KE and momentum and `E_fand p_f` are respectively final KE and momentum then

`E_i =p_i^2/(2m)`

and

`E_f =p_f^2/(2m)`

combining these two we have

`E_f/E_i=p_f^2/p_i^2`

By the given condition `p_f=50%of p_i=p_i/2`

so

`E_f/E_i=p_f^2/(2p_f)^2=1/4`

`=>(E_f-E_i)/E_i=-3/4=-75%`

So change in KE is 75% , here negative sign denotes the decrease in KE