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Q.

A thin uniform rod of length $ℓ$ and mass $m$ is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $ω .$ Its centre of mass rises to a maximum height of

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a

$\frac{1}{6} \frac{ℓ^{2} ω^{2}}{g}$

b

$\frac{1}{6} \frac{ℓ ω}{g}$

c

$\frac{1}{3} \frac{ℓ^{2} ω^{2}}{g}$

d

$\frac{1}{2} \frac{ℓ^{2} ω^{2}}{g}$

answer is D.

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Detailed Solution

$T . E_{i} = T . E_{f}$

$\frac{1}{2} l ω^{2} = m g h$

$\frac{1}{2} \times \frac{1}{3} m ℓ^{2} ω^{2} = m g h \Rightarrow h = \frac{1}{6} \frac{ℓ^{2} ω^{2}}{g}$

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