Question

A rod AB of weight  is placed over a sphere of weight as shown in figure. Ground is rough and there is no friction between rod and sphere and sphere and wall. Draw free body diagrams of sphere and rod separately.

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Hard

Solution

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Given,
Lac <  Lcb
Also, Weight of rod of length  is
Let weight of part ac be and of part cb be .
therefore,
= ( Lac / L )
and, = ( Lcb / L)
clearly, < (since, Lac < Lcb)
Therefore, rod will tend to move anticlockwise,
Thus friction at contact point of rod and ground will act in backward direction.

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