Consider the situation shown in the figure. Uniform rod of length… - Vidyadip

MCQ

Consider the situation shown in the figure. Uniform rod of length $L$ can rotate freely about the hinge $A$ in vertical plane. Pulleys and string are light and frictionless. If therod remains horizontal at rest when the system is released then the mass of the rod is :

A
$\frac{4}{3} M$
B
$\frac{8}{3} M$
✓
$\frac{16}{3} M$
D
$\frac{32}{3} M$

✓

Answer

Correct option: C.

$\frac{16}{3} M$

c
$\mathrm{T}=\frac{2 \mathrm{M}_{1} \mathrm{M}_{2} \mathrm{g}}{\mathrm{M}_{1}+\mathrm{M}_{2}}$

$\mathrm{T}=\frac{2 \mathrm{Mg}}{3}$

Balancing torque

$\mathrm{M}_{\mathrm{g}} \times \frac{\mathrm{L}}{2}=\frac{4 \mathrm{Mg}}{3} \times \mathrm{L}$

$\frac{M^{\prime}}{2}=\frac{4 M}{3}$

$M^{\prime}=\frac{8 M}{3}$

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