First slide

Dynamics of rotational motion about fixed axis

Question

A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q as shown in figure. When string is cut, the initial angular acceleration of the rod is [NEET 2013)

Moderate

A

$\frac{3 g}{2 L}$
B

$\frac{g}{L}$
C

$\frac{2 g}{L}$
D

$\frac{2 g}{3 L}$

Solution

When the string is cut, the rod can be shown as
Torque on the rod = Moment of weight of the rod about P,
$τ = M g \frac{L}{2}$ …(i)
$∵$ Moment of inertia of rod about $P, I = \frac{M L^{2}}{3}$ . ..(ii)
As, $τ = I α$
From Eqs. (i) and (ii), we get
$M g \frac{L}{2} = \frac{M L^{2}}{3} α$
$∴$ The initial angular acceleration of the rod, $α = \frac{3 g}{2 L}$

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