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A block of mass m is placed on a surface with a vertical cross section given by y = x³/6. If the coefficient of friction is 0.5, then maximum height above the ground at which the block can be placed without slipping is -

1. 2/3 m
2. 1/3 m
3. 1/2 m
4. 1/6 m

Correct answer: 1/6 m

Solution

The maximum height at which the block can be placed without slipping is determined by balancing the gravitational force and the frictional force. Given the surface's slope and the coefficient of friction, the calculations show that the maximum height is 1/6 m, as this is the point where the frictional force is sufficient to counteract the component of gravitational force acting parallel to the surface.

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