A uniform rod of mass m and length l is suspended by two strings at its ends as shown. When one of the strings is cut, the rod starts falling with an initial angular acceleration

Question

A uniform rod of mass m and length l is suspended by two strings at its ends as shown. When one of the strings is cut, the rod starts falling with an initial angular acceleration (A) (g/l) (B) (g/2 l) (C) (3 g/2 l) (D) (3 g/4 l)

Tardigrade Admin · Accepted Answer

τ=I α (m g l/2)=(m l2/3) α α=(3 g/2 l) and a=α r =(l/2) ⋅ (3 g/2 l)=(3 g/4)

Q. A uniform rod of mass $m$ and length $l$ is suspended by two strings at its ends as shown. When one of the strings is cut, the rod starts falling with an initial angular acceleration

$\frac{g}{l}$

$\frac{g}{2 l}$

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

$\frac{3 g}{4 l}$

$τ = I α$
$\frac{m g l}{2} = \frac{m l ^{2}}{3} α$
$α = \frac{3 g}{2 l}$ and $a = α r$
$= \frac{l}{2} \cdot \frac{3 g}{2 l} = \frac{3 g}{4}$

Q. A uniform rod of mass m and length l is suspended by two strings at its ends as shown. When one of the strings is cut, the rod starts falling with an initial angular acceleration

lg​

2lg​

2l3g​

4l3g​