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A block slides down a rough inclined plane of length l and angle of inclination θ. If the coefficient of friction between the block and the plane is μ, what is the speed of the block when it reaches the lower end of the plane?

1. [2g(lμ cos θ − l sin θ)]¹/2
2. [2g(l sin θ − μ cos θ)]¹/2
3. [2g(l sin θ + μ cos θ)]¹/2
4. [2g(l cos θ + μ sin θ)]¹/2

Correct answer: [2g(l sin θ − μ cos θ)]¹/2

Solution

The correct option accounts for the net force acting on the block as it slides down the incline, which includes the gravitational component along the incline and the opposing frictional force. By applying energy conservation principles and considering the work done against friction, the derived expression accurately reflects the block's speed at the bottom of the incline.

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