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Viscous Force

Four solid sp...

Question

Four solid spheres are made to move on a rough horizontal surface. Sphere $P$ is given a spin and released. Sphere $Q$ is given a forward linear velocity. Spheres $R$ and $S$ are given linear and rotational motions as shown in the figure. Directions of the friction force on spheres $P, Q, R, S$ are respectively.
Diagram

A

Left, Right, Left, either Left or Right

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B

Right, Left, Left, either Left or Right

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C

Right, Left, Left, Right

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D

Right, Left, Right, Left

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Solution

The correct option is B Right, Left, Left, either Left or Right
In sphere $P$ , the point of contact has tendency to move towards left with respect to surface and hence, friction acts on it towards right.
In spheres $Q$ and $R$ , the point of contact has tendency to move towards right with respect to surface and hence, friction acts on both of them towards left.
In sphere $S$ , the point of contact has tendency to move towards left due to rotation and towards right due to translatory motion. It has not been specified in question whether $v$ is less than or greater than $ω R$ . Hence, friction on it may act towards left or right.

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