Question #26e1f

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Answer 1 · 2017-05-12T04:29:49

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