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A block of mass m rests on a surface whose vertical profile is described by y = x³/6. If the coefficient of friction is 0.5, what is the greatest height above the ground at which the block can be placed so that it does not slide?

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

Correct answer: 1/6 m

Solution

The correct option is 1/6 m because at this height, the gravitational force acting on the block is balanced by the maximum static friction force, which is determined by the coefficient of friction and the normal force. As the height increases, the angle of the surface increases, leading to a greater component of gravitational force parallel to the surface, which can cause the block to slide.

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