A ball of mass m moving with speed u undergoes a head-on elastic collision with a ball of mass n m initially at rest. The fraction of the incident energy transferred to the second ball is

Question

A ball of mass m moving with speed u undergoes a head-on elastic collision with a ball of mass n m initially at rest. The fraction of the incident energy transferred to the second ball is (A) (n/1+n) (B) (n/(1+n)2) (C) (2 n/(1+n)2) (D) (4 n/(1+n)2)

Tardigrade Admin · Accepted Answer

As the collision is elastic, we can find

v_{1} = \frac{1 - n}{1 + n} u, v_{2} = \frac{2 u}{1 + n}

Hence, the required fraction is

\frac{\frac{1}{2} nm v _{2}^{2}}{\frac{1}{2} m u ^{2}} = n (\frac{v _{2}}{u})^{2}

= \frac{4 n}{( 1 + n ) ^{2}}

Q. A ball of mass $m$ moving with speed $u$ undergoes a head-on elastic collision with a ball of mass $nm$ initially at rest. The fraction of the incident energy transferred to the second ball is

$\frac{n}{1 + n}$

$\frac{n}{( 1 + n ) ^{2}}$

$\frac{2 n}{( 1 + n ) ^{2}}$

$\frac{4 n}{( 1 + n ) ^{2}}$

As the collision is elastic, we can find
$v_{1} = \frac{1 - n}{1 + n} u, v_{2} = \frac{2 u}{1 + n}$

Hence, the required fraction is
$\frac{\frac{1}{2} nm v _{2}^{2}}{\frac{1}{2} m u ^{2}} = n (\frac{v _{2}}{u})^{2}$
$= \frac{4 n}{( 1 + n ) ^{2}}$

Q. A ball of mass m moving with speed u undergoes a head-on elastic collision with a ball of mass nm initially at rest. The fraction of the incident energy transferred to the second ball is

1+nn​

(1+n)2n​

(1+n)22n​

(1+n)24n​