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Q.

A small mass slides down an inclined plane of inclination θ with the horizontal. The coefficient of friction is μ = μ0 x where x is the distance through which the mass slides down and μ0,  a constant. Then the mass has maximum speed after the mass covers a distance of

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a

cos θμo

b

sin θμo

c

tan θμ0

d

2 tan θμ0

answer is C.

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Detailed Solution

Acceleration of mass at distance x,

a = g(sinθ-μ0 x cosθ)

Speed is maximum, when a = 0

⇒ g(sin θ - μ0x cosθ) = 0

⇒x = tan θμ0

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