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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
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B
3l/4
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C
l/2
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D
2l/3
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Solution

The correct option is D 2l/3
Draw a diagram of given problem.

Calculate x for rod.
Impulse = change in momentum.
J=mv (i)
Where, v is linear speed of center of mass of rod.
Similarly,
Jx=Iω=ml23ω (ii)
v=l2ω (iii)
Solving all three above equations, we get
x=23l

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