Question

Two masses each with mass $0.10\text{kg}$ are moving with velocity $3\text{m/s}$ along $x$ axis and $5\text{m/s}$ along $y$ axis respectively. After an elastic collision, one of the masses moves with a velocity $4\hat{i}+4\hat{j}$. The energy of the other mass after collision is $\frac{x}{10}\text{J}$. Then $x$ is

Answer 1

As we know,
For elastic collision, $K{E}_i=K{E}_f$
Assume speed after collision is $v_1$ and $v_2$.
Given, $v_1=\sqrt{4^2+4^2}=\sqrt{32}$

$K{E}_i=K{E}_f$
$\Rightarrow \frac{1}{2}\times m\times (5{)}^2+\frac{1}{2}\times m\times (3{)}^2=\frac{1}{2}\times m\times (\sqrt{32}{)}^2+\frac{1}{2}\times m\times v_2^2$
$\Rightarrow 34=32+v_2^2$
$\Rightarrow v_2^2=2$
Hence, K.E. of second mass after collision is
$KE=\frac{1}{2}m(v_2{)}^2=\frac{1}{2}\times 0.1\times 2=0.1\text{J}=\frac{1}{10}$
Thus, $x=1$