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Q.

A block of mass M slides down a rough inclined surface of inclination 'θ‘ and reaches the bottom at speed ’v'. However, if it slides down a smooth inclined surface of same length and same inclination, it reaches the bottom with speed kv. Coefficient of friction between the block and the rough incline is:

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a

sin⁡θk2−1

b

k2−1k2tan⁡θ

c

k2+1k2cos⁡θ

d

k2−1k2

answer is B.

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Detailed Solution

v=2g(sin⁡θ−μcos⁡θ)s and kv=2gsin⁡θs
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A block of mass M slides down a rough inclined surface of inclination 'θ‘ and reaches the bottom at speed ’v'. However, if it slides down a smooth inclined surface of same length and same inclination, it reaches the bottom with speed kv. Coefficient of friction between the block and the rough incline is: