Question

A sphere rolls without slipping on a rough horizontal surface with centre of mass speed $v_0$. If mass of the sphere is $M$ and its radius is $R$, then what is the angular momentum of the sphere about the point of contact?

• A. $\frac{5}{2}M{v}_{o}R$
• B. $\frac{3}{5}M{v}_{o}R$
• C. $\frac{7}{5}M{v}_{o}R$
• D. $\frac{1}{2}M{v}_{o}R$

Answer 1

The correct option is C $\frac{7}{5}M{v}_{o}R$

Draw a diagram of given problem.

Calculate angular momentum of sphere.

Formula used: $L=m{v}_{0}R+l\omega$
Using formula,
$L=m{v}_{0}R+I\omega$
$=m{v}_{0}R+\frac{2}{5}M{R}^2\omega$
$=m{v}_{0}R+\frac{2}{5}M{R}^2\frac{v_0}{R}$
$L=\frac{7}{5}m{v}_{0}R$