Question

In the figure, a sphere of radius $2 \, m$ rolls on a plank. The accelerations of the sphere and the plank are indicated. The value of angular acceleration is

• A. $2rads^{- 2}$
• B. $4rads^{- 2}$
• C. $3rads^{- 2}$
• D. $1rads^{- 2}$

Answer 1

Answer: (C)

As the sphere rolls, the lowest point of the sphere should have the same acceleration as the plank.
Hence, $a_{1}=αR-a_{2}$
$2=2\alpha -4$
$\Rightarrow \alpha =3rads^{- 2}$