A block of mass m is released from the top of a rough inclined plane as shown in the figure. Coefficient of friction between the block and the plane is μ. Speed of the block at the bottom of the plane is v.
A
Block will reach bottom if l≥μd
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B
Work done by friction is independent of l
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C
Work done by friction is independent of d
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D
v=√2g(l−μd)
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Solution
The correct options are A Block will reach bottom if l≥μd B Work done by friction is independent of l D v=√2g(l−μd)
fl=μN=μmgcosθ wf=∫fdl=∫umgcosθdl wf=∫umgdx=μmgd By work energy theorem, ⇒mgl−μmgd=12mv2 ⇒v=√2g(l−μd)