Question

A coin of mass $10g$ rolls along a horizontal table with a velocity of $6cm/s$ . Its total kinetic energy is

• A. $9\mu J$
• B. $18\mu J$
• C. $27\mu J$
• D. $36\mu J$

Answer 1

Answer: (C)

The total kinetic energy of the coin is
$K=K_{\tau }+K_R$
$=\frac{1}{2}m{v}^2+\frac{1}{2}I{\omega }^2$
For coin, the moment of inertia
$I=\frac{1}{2}M{R}^2$
$\therefore K=\frac{1}{2}M{v}^2+\frac{1}{4}M{v}^2$
$(\because v=r\omega )$
$=\frac{3}{4}M{v}^2$
$=\frac{3}{4}\times \left(10\times 10^{-3}\right){\left(6\times 10^{-2}\right)}^2$
$=27\times 10^{-6}J=27\mu J$