A uniform metre stick of mass M is hinged at one end and supported in a horizontal direction by a string attached to the other end. What should be the initial acceleration (in rad / s 2) of the stick if the string is cut?

Question

A uniform metre stick of mass M is hinged at one end and supported in a horizontal direction by a string attached to the other end. What should be the initial acceleration (in rad / s 2) of the stick if the string is cut? (A) (3 g/2 L) (B) g / L (C) 3 g / L (D) 4 g / L

Tardigrade Admin · Accepted Answer

τ=I α=M g (L/2) (M L2/3) α=(M g L/2) ⇒ α=(3 g/2 L) rad / sec 2

Q. A uniform metre stick of mass $M$ is hinged at one end and supported in a horizontal direction by a string attached to the other end. What should be the initial acceleration (in $r a d / s^{2})$ of the stick if the string is cut?

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

$g / L$

$3 g / L$

$4 g / L$

$τ = I α = M g \frac{L}{2}$
$\frac{M L ^{2}}{3} α = \frac{M gL}{2}$
$\Rightarrow α = \frac{3 g}{2 L} r a d / se c^{2}$

Q. A uniform metre stick of mass M is hinged at one end and supported in a horizontal direction by a string attached to the other end. What should be the initial acceleration (in rad/s2) of the stick if the string is cut?

2L3g​

g/L

3g/L

4g/L