Question

A particle of mass $m$ strikes a wall elastically with speed $v$ at an angle ${30}^o$ with the wall as shown in the figure. The magnitude of impulse imparted to the ball by the wall is:

• A. $mv$
• B. $\frac{mv}{2}$
• C. $2mv$
• D. $\sqrt{3}mv$

Answer 1

The correct option is A $mv$

Before the particle strike,

Linear momentum perpendicular to the wall$=mvsin\left({30}^o\right)=\frac{mv}{2}$

Linear momentum along to the wall$=mvcos\left({30}^o\right)$

After the particle strike,

Linear momentum perpendicular to the wall$=-mvsin\left({30}^o\right)=-\frac{mv}{2}$

Linear momentum along to the wall$=mvcos\left({30}^o\right)$

Impulse=change in linear momentum,

Linear Momentum changed only perpendicular to the wall.

$\Rightarrow Impulse=-\frac{mv}{2}-\frac{mv}{2}=-mv$

Magnitude of Impulse is $mv$