Question

A thin metal disc of radius 0.25 m and mass 2 kg starts from rest and rolls down an inclined plane. If its rotational kinetic energy is 4 J at the foot of the inclined plane, then the liner velocity at the same point is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$\Rightarrow$ 4 = $\frac{1}{2}$ $I_c$ $w^2$

Where $I_c$ $\frac{M{R}^2}{2}$

$\Rightarrow$ 8 = $\frac{M{R}^2{w}^2}{2}$ w = $\sqrt{\frac{16}{M{R}^2}}$ = 8 $\sqrt{2}$

Asper Rolling Condition , $V_{cm}$ R w

$\Rightarrow$ $V_{cm}$ = $\frac{1}{4}$ (8 $\sqrt{2}$) = 2$\sqrt{2}$ m/s