Question

A ring and a disc have the same mass and roll without slipping with the same linear velocity $v$. If the total kinetic energy of the loop is $8J$, the kinetic energy of disc is

• A. $8J$
• B. $6J$
• C. $16J$
• D. $4J$

Answer 1

The correct option is B $6J$

$v=Rw$ (no slipping)

Total K.E, $E=\frac{1}{2}I{w}^2+\frac{1}{2}m{v}^2$

For Ring: $I=m{r}^{2}E=8J$

$8=\frac{1}{2}m{r}^2{w}^2+\frac{1}{2}m{v}^2$

$8=\frac{1}{2}m{v}^2+\frac{1}{2}m{v}^2⟹m{v}^2=8$ .......................(1)

For disc: $I=\frac{1}{2}m{R}^2$

$E=\frac{1}{4}m{R}^2{w}^2+\frac{1}{2}m{v}^2$

$E=\frac{1}{4}m{v}^2+\frac{1}{2}m{v}^2$

$E=\frac{3}{4}m{v}^2=\frac{3}{4}\times 8=6J$