Question

If the translatory kinetic energy of a rolling solid sphere is $35J$, then its total kinetic energy is:

• A. $42J$
• B. $49J$
• C. $56J$
• D. $63J$

Answer 1

Answer: (B)

$49J$

Given $\frac{1}{2}m{v}^2=35J$
$v=rw$
Rotational kinetic energy of solid sphere is $R=\frac{1}{2}I{w}^2$
$I=\frac{2}{5}m{r}^2$
$R=\frac{1}{2}\times \frac{2}{5}m{r}^2\times w^2$
$=\frac{1}{5}m{r}^2{w}^2$
$=\frac{1}{5}m{v}^2$
Total Kinetic energy $=$ Rotational Kinetic energy + Translational kinetic energy
$=\frac{1}{5}m{v}^2+\frac{1}{2}m{v}^2$
$=\frac{7}{10}m{v}^2$
$KE=\frac{1}{2}m{v}^2\times \frac{7}{5}$
$KE=49J$