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A block of mass m is placed on a smooth wedge of inclination θ. The whole system is accelerated horizontally so that the block does not slip on the wedge. The force exerted by the wedge on the block (g is acceleration due to gravity) will be

1. mg cos θ
2. mg cos θ
3. mg sin θ
4. mg

Correct answer: mg cos θ

Solution

The block remains stationary relative to the wedge, so the net force on the block must be perpendicular to the wedge. The normal force exerted by the wedge balances the component of gravitational force and the pseudo force due to horizontal acceleration. This results in the force exerted by the wedge being equal to mg cos θ.

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