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Question

A person throws a stick of length 2 m such that the centre of the stick is moving vertically upwards with a velocity 5 m/s and the angular velocity of the stick about its centre is 10 rad/s. Find the magnitude of velocity of end A of the rod when COM of the rod reaches maximum height.


A
zero
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B
5 m/s
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C
10 m/s
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D
15 m/s
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Solution

The correct option is C 10 m/s
At maximum height, the vertical component of velocity of COM will be zero.
i.e VO=0 ...(i)
Length of rod, L=2 m
Hence, velocity of end A at maximum height,
VA=VO+VAO ...(ii)
|VAO|=rω=L2×ω=1×10=10 m/s
From Eq (i) & (ii),
VA=VAO
|VA|=|VAO|
|VA|=10 m/s

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