Question

A sphere rolls down without slip on an inclined plane of inclination $\theta .$ What is a linear acceleration as the sphere reaches the bottom?

• A. $\frac{5}{7}gsin\theta$
• B. $\frac{3}{5}gsin\theta$
• C. $\frac{2}{7}gsin\theta$
• D. $\frac{2}{9}gsin\theta$

Answer 1

The correct option is A $\frac{5}{7}gsin\theta$

Solution

REF.Image

ABD will be as:

$\propto R=a$ [Pure Rolling] ___ (i)

Torque = $I\propto$

$\Rightarrow \left(fs\right)\left(R\right)=\left(\frac{2}{5}\right)M{R}^2\propto$

$\Rightarrow fs=\frac{2}{5}(R\propto )$ ___ (ii)

Also $mgsin\theta -fs=ma$ ___ (iii)

From (i), (ii) and (iii)

$mgsin\theta -\frac{2}{5}ma=ma$

$\Rightarrow \frac{5}{7}gsin\theta =a$

Option - A is correct.