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Question
A sphere is rotating about a diameter.
Options
The particles on the surface of the sphere do not have any linear acceleration.
The particles on the diameter mentioned above do not have any linear acceleration.
Different particles on the surface have different angular speeds.
All the particles on the surface have same linear speed.
Solution
The particles on the diameter mentioned above do not have any linear acceleration.
Explanation:-
Linear acceleration of a rotating particle is given as
\[\overrightarrow{a} = \overrightarrow{r} \times \overrightarrow{\alpha}\]
The sphere is rotating about a diameter; therefore, the position vector of the particles on the diameter is zero. Thus, linear acceleration of the particle is zero.
Explanation of other options:- All the particles of the body have the same angular velocity. All the particle on the surface have different linear speeds that depend on the position of the particle from the axis of rotation.
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