A long uniform rod of length L and mass M is pivoted vertically on...

A long uniform rod of length

L

and mass

M

is pivoted vertically on a horizontal, friction less pivot at its lower end. The rod is released from rest in its vertical position OA (see figure). It falls off without slipping at O . At the instant the rod is horizontal, A long uniform rod of length L and mass M is pivoted vertically on a horizontal, friction less pivot at its lower end.

A long uniform rod of length L and mass M is pivoted vertically on a horizontal, friction less pivot at its lower end.

Options

AIts angular speed is $\sqrt{\frac{3 \mathrm{~g}}{\mathrm{~L}}}$
BMagnitude of its angular acceleration is $\frac{3 \mathrm{~g}}{2 \mathrm{~L}}$
CAcceleration of its centre of mass $\mathrm{a}_{\mathrm{CM}}=-\frac{3 \mathrm{~g}}{4} \hat{\mathrm{j}}(\hat{\mathrm{j}}$ unit vector in Y direction)
DReaction force at pivot $=\frac{M g}{4} \hat{j}$ (Take $X, Y$ axis as shown)

Correct answer

B. Magnitude of its angular acceleration is $\frac{3 \mathrm{~g}}{2 \mathrm{~L}}$

Step-by-step solution

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