Question

A solid sphere of mass $2kg$ rolls on a smooth horizontal surface at $10m/s$. It then rolls up a smooth inclined plane of inclination ${30}^o$ with the horizontal. The height attained by the sphere before it stops is?

• A. $700cm$
• B. $701cm$
• C. $7.1cm$
• D. $Noneofthese$

Answer 1

The correct option is D $Noneofthese$

Mechanical energy is conserved.
u = initial velocity
v = final velocity = 0
h = initial height
d = final height
m = mass
g = $10m/s^2$

$\frac{1}{2}{mu}^2+mgh=\frac{1}{2}{mv}^2+mgd$

dividing by m on both sides and substituting values,

$\frac{1}{2}\times {10}^2+10\times 0=\frac{1}{2}{\times 0}^2+10d$

$10d=\frac{100}{2}=50$

$d=\frac{50}{10}=5meters$

conclusion: hence the option (D) is correct.