Question

A rolling object rolls without slipping down an inclined plane (angle of inclination $\theta$), then the minimum acceleration it can have is

• A. $\frac{2g\sin \theta }{3}$
• B. $g\sin \theta$
• C. $\frac{g\sin \theta }{2}$
• D. zero

Answer 1

The correct option is C $\frac{g\sin \theta }{2}$

Let the mass of the rolling object be m and radius $R$.
As we know,
$a=\frac{g\sin \theta }{1+\frac{1}{M{R}^2}}$
Acceleration will be minimum when the moment of inertia is maximum.
$a_{\text{min}}=\frac{g\sin \theta }{1+\frac{M{R}^2}{M{R}^2}}$

$=\frac{g\sin \theta }{2}$
($I_{\text{max}}=M{R}^2$ for ring)

Final answer:(c)