Question

When a body slides down from rest along a smooth inclined plane making an angle of 45° with the horizontal, it takes time T. When the same body slides down from rest along a rough inclined plane making the same angle and through the same distance, it is seen to take time pT, where p is some number greater than 1. Calculate the co-efficient of friction between the body and the rough plane.

Answer 1

Explanation:

Correct option is

B

μ=(1−1/p

2

)

Given Situations are shown in figure,

For smooth inclined plane,

Here, Mgsinθ=Ma

⇒a=gsinθ

Let s=length of inclined plane

Using, s=ut+

2

1

at

2

⇒s=0×T+

2

1

(gsinθ)T

2

(∵t=T)

⇒s=

2

1

gsinθT

2

⇒s=

2

2

1

gT

2

(∵θ=45

0

) ...(i)

For rough inlined plane.

f=μN=μMgcosθ

Mgsinθ−f=Ma

′

⇒a

′

=(sinθ−μcosθ)g

Using S=ut+

2

1

a

′

t

2

s=0×(pT)+

2

1

(sinθ−μcosθ)g×p

2

T

2

(\because t=pT)

s=

2

2

1

(1−μ)gp

2

T

2