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Question: A block is kept on an inclined plane of inclination θ of length l. The velocity of particle at the b...

A block is kept on an inclined plane of inclination θ of length l. The velocity of particle at the bottom of inclined is (the coefficient of friction is μ)

A

2gl(μcos⁡θ−sin⁡θ)\sqrt { 2 g l ( \mu \cos \theta - \sin \theta ) }

B

2gl(sin⁡θ−μcos⁡θ)\sqrt { 2 g l ( \sin \theta - \mu \cos \theta ) }

C

2gl(sin⁡θ+μcos⁡θ)\sqrt { 2 g l ( \sin \theta + \mu \cos \theta ) }

D

2gl(cos⁡θ+μsin⁡θ)\sqrt { 2 g l ( \cos \theta + \mu \sin \theta ) }

Answer

2gl(sin⁡θ−μcos⁡θ)\sqrt { 2 g l ( \sin \theta - \mu \cos \theta ) }

Explanation

Solution

Acceleration (1) =g(sin⁡θ−μcos⁡θ)= g ( \sin \theta - \mu \cos \theta ) and s = l

v=2asv = \sqrt { 2 a s } =2gl(sin⁡θ−μcos⁡θ)= \sqrt { 2 g l ( \sin \theta - \mu \cos \theta ) }