Question

A uniform rod of length 0.72 m is pivoted at one end is hanging as shown. It receives a horizontal impulse at a distance x below the pivot as shown. If impulse applied by the pivot is zero, then find the value of $x$(in cm ).

Answer 1

Given: A uniform rod of length 0.72 m is pivoted at one end is hanging as shown. It receives a horizontal impulse at a distance x below the pivot as shown. If impulse applied by the pivot is zero,

To find the value of x(in cm ).

Solution:

Conserving the angular momentum about pivot,

$J.x=I\omega$

$⟹J.x=\frac{m{l}^2}{3}\omega$

But we know,

$J=\frac{ml\omega }{2}$

Substituting the value of J in above equation we get

$\frac{ml\omega }{2}.x=\frac{m{l}^2}{3}\omega ⟹x=\frac{2l}{3}$

Now substituting the value of l=0.72m, we get

$x=\frac{2\times 0.72}{3}⟹x=0.48m=48cm$

Hence horizontal impulse at a distance of 48 cm below the pivot is applied.