Question

A solid sphere starts rolling down on an inclined plane from a vertical height $3.5m$. The velocity of centre of mass of sphere on reaching the bottom of inclined plane is :

• A. $2.45m{s}^{-1}$
• B. $4.9m{s}^{-1}$
• C. $7m{s}^{-1}$
• D. $9.8m{s}^{-1}$

Answer 1

Answer: (C)

$7m{s}^{-1}$

Apply Work Energy Theorem.

Loss in gravitational potential energy = gain in rotational kinetic energy +gain in translational kinetic energy
$mgh=\frac{1}{2}m{V}^2+\frac{1}{2}\left(\frac{2}{5}m{R}^2\right){\left(\frac{V}{R}\right)}^2$
$mgh=\frac{1}{2}\times \frac{7}{5}\times m{V}^2$
$\sqrt{2\times 5\times \frac{(3.5\times 10)}{7}}=V$
$V=5\sqrt{2}m/s$
$=7.07m/s$