System Of Particles And Rotational Motion Ques 83

Answer:

Correct Answer: 83.(c)

Solution:

83. (c)

From law of conservation of mechanical energy,

$\Rightarrow \frac{1}{2} I \omega^{2}+0+\frac{1}{2} mv^{2}=mg \times \frac{3 v^{2}}{4 g}$

$\Rightarrow \frac{1}{2} I \omega^{2}=\frac{3}{4} mv^{2}-\frac{1}{2} mv^{2}$

$\Rightarrow \frac{1}{2} I \omega^{2}=\frac{mv^{2}}{2}(\frac{3}{2}-1)$

or, $\frac{1}{2} I(\frac{V^{2}}{R^{2}})=\frac{mv^{2}}{4}$ or, $I=\frac{1}{2}$ $ mR^{2}$

Hence, object is a disc.