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 figure, impulse delivered by pivot is zero if $x$ is equal to

• A. $\frac{l}{2}$
• B. $\frac{l}{3}$
• C. $\frac{2l}{3}$
• D. $\frac{3l}{4}$

Answer 1

Answer: (C)

$\frac{2l}{3}$

Applying the law of conservation of angular momentum on the body at the pivot:

Taking the mass of uniform rod as $m$,

At point A on the rod, as there is no impulse:

$\therefore J=\frac{m\times l\times \omega }{2}$

At point of strike on the rod:

$J\times x=\frac{m\times l^2\times \omega }{3}$

$\Rightarrow x=\frac{2l}{3}$