Question

Two identical spheres $A$ and $B$ each of mass $M$ and radius $R$ are moving on a horizontal surface as shown. The angular momentum of the sphere $A$ about the topmost point of the sphere $B$ is

• A. $MvR$
• B. $MvR+\frac{2}{5}M{R}^2\omega$
• C. $MvR+\frac{7}{5}M{R}^2\omega$
• D. None of these

Answer 1

The correct option is B $MvR+\frac{2}{5}M{R}^2\omega$

$\begin{array}{c}\text{Angulare momentum of sphere A about its own axis-}\\ \begin{array}{cc}L=\frac{2}{5}M{R}^2\cdot \omega & \text{sinu}L=I\omega \\ I\to \text{Moment of Inertia}& \end{array}\end{array}$

$\begin{array}{c}\text{Therefore angularmomentum of sbhere A about}\\ \text{boint}P\text{will be-}\\ \begin{array}{c}L=I\omega +Mvdd\to \text{Perpendicular distanu}\\ \text{ot centre to the paralue}\\ \text{line passing through}P.\end{array}\end{array}$

$\begin{array}{c}\text{Here}d=R\text{from the diagram}\\ \text{Henu,}L=MVR+\frac{2}{5}M{R}^2\omega \end{array}$