Question

A circular disc of mass $2kg$ and radius $10cm$ rolls without slipping with a speed $2m/s$. The total kinetic energy of disc is

• A. $10J$
• B. $6J$
• C. $2J$
• D. $4J$

Answer 1

The correct option is B $6J$

Given mass $m=2kg$, Radius $R=10cm=0.1m$, Speed $v=2m/s$

Disc is rolling without slipping $\Rightarrow v=R\omega$

Translational Kinetic Energy (TKE) $=\frac{1}{2}m{v}^2=\frac{1}{2}\times 2\times 2^2=4J$

Rotational Kinetic Energy (RKE) $=\frac{1}{2}I{\omega }^2=\frac{1}{2}\left(\frac{m{R}^2}{2}\right)\times {\left(\frac{v}{R}\right)}^2=\frac{1}{4}m{v}^2=2J$

$\Rightarrow$ Total Energy= TKE + RKE$=4+2=6J$