Question

A uniform rod of length $l$ is pivoted at point $A$. It is struck by a horizontal force which delivers an impulse $J$ at a distance $x$ from point $A$ as shown in the figure, impulse delivered by pivot is zero if $x$ is equal to

• A. $l/3$
• B. $3l/4$
• C. $l/2$
• D. $2l/3$

Answer 1

The correct option is D $2l/3$

Draw a diagram of given problem.

Calculate $x$ for rod.
Impulse = change in momentum.
$J=mv\left(i\right)$
Where, $v$ is linear speed of center of mass of rod.
Similarly,
$J\cdot x=I\omega =\frac{m{l}^2}{3}\omega \left(ii\right)$
$v=\frac{l}{2}\omega \left(iii\right)$
Solving all three above equations, we get
$x=\frac{2}{3}l$