Question

A particle of mass $m$ moving with a velocity $(3\hat{i}+2\hat{j})m{s}^{-1}$ collides with a stationary body of mass $M$ and finally moves with a velocity $(-2\hat{i}+\hat{j})m{s}^{-1}$. If $\frac{M}{m}=\frac{1}{13}$, then:

• A. the impuse received by $M$ is $m(5\hat{i}+\hat{j})$
• B. The velocity of the $M$ is $\frac{1}{13}(5\hat{i}+\hat{j})$
• C. The coefficient of restitutions $\frac{11}{17}$
• D. All of the above are correct

Answer 1

The correct option is A the impuse received by $M$ is $m(5\hat{i}+\hat{j})$

Impulse = change in momentum

$\begin{array}{c}=m.\Delta V\\ =m\left[\left(3\hat{i}+2\hat{j}\right)-\left(-2\hat{i}+\hat{j}\right)\right]\\ =m\left[5\hat{i}-\hat{j}\right].\end{array}$