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Q.

A uniform rod $A B$ is hinged at one end $A$ . The rod is kept in the horizontal position by a massless string tied to point $B$ as shown. Find the reaction $(R_{A})$ of the hinge on the end $A$ of the rod and the angular acceleration $(α)$ at the instant when string is cut.

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a

$R_{A} = \frac{m g}{2}$

b

$R_{A} = \frac{m g}{4}$

c

$α = \frac{2 g}{3 l}$

d

$α = \frac{3 g}{2 l}$

answer is A, D.

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Detailed Solution

$τ_{A} = m g \frac{l}{2} . . . . . . . (i) τ_{A} = I α . . . . . . . (i i) I α = m g \frac{l}{2} α = m g \frac{l}{\frac{2}{I}} H e r e I = \frac{m l^{2}}{3} α = \frac{m g l / 2}{\frac{m l^{2}}{3}} = \frac{3}{2} \frac{g}{l} a_{c m} = a r = \frac{3}{2} \frac{g}{l} x \frac{l}{2} = \frac{3 g}{4} = \frac{3 g}{4} m g - R_{A} = m a_{c m} m g - R_{A} = m x \frac{3 g}{4} R_{A} = \frac{m g}{4}$

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