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Question

A given object takes n times as much time to slide down a 45o incline rough plane as on a smooth plane of same inclination. The coefficient of Kinetic friction between the object and the incline is given by:

A
(11n2)
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B
(11n2)
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C
112
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D
11n2
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Solution

The correct option is A (11n2)

Given,

Time taken by object to slide on frictionless incline plane is T

Time taken by object to slide on rough incline plane is nT

Net acceleration on smooth incline plane, a=gsinθ

Apply kinematic equation

s=ut+12at2

s=0+12gsinθ×T2.... (1)

Net acceleration on rough inclined plane a=gsinθμcosθ

Apply kinematic Equation.

s=ut+12at2

s=0+12(gsinθμgcosθ)×(nT)2

Put value of s from equation (1)

12gsinθ×T2=12(gsinθμgcosθ)(nT)2

1=(1μtan45o)n2

μ=(11n2)

Coefficient of friction μ=(11n2)


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