Question

A solid sphere of mass $1\text{kg}$ and radius $10\text{cm}$ rolls down an inclined plane of height $7\text{m}$. The velocity of its center as it reaches the ground level is

• A. $7\text{m/s}$
• B. $10\text{m/s}$
• C. $15\text{m/s}$
• D. $20\text{m/s}$

Answer 1

The correct option is B $10\text{m/s}$


$T{E}_{initial}=PE=mgh$


$T{E}_{final}=PE+K_T+K_r$
$=\frac{1}{2}m{v}^2+\frac{1}{2}I{w}^2$

$\frac{1}{2}m{v}^2+\frac{1}{2}\times \frac{2}{5}m{r}^2\times \frac{v^2}{r^2}$

$T{E}_i=T{E}_f$
$\mathrm{mgh}=\frac{7}{10}{mv}^2$
$10\times 7=\frac{7}{10}{v}^2$

$⟹v=10m/s^2$