Question

A body slides down on an inclined
plane of inclination 45º from rest. The time taken
to cover a certain distance in the absence of fric-
tion is half of the time taken to cover the same dis-
tance in the presence of friction. Find the coeffi-
cient of friction.​

Answer 1

Case (1) When there is no friction,

From newton's second law, F=ma

⇒mgsinθ=ma

1

⇒a

1

=gsinθ

Now, as body starts from rest so initial velocity (u)=0 m/s.

Let, body travels 'x' distance in t

1

time,

So from equation of motion,

x=ut+

2

1

at

2

⇒x=

2

1

a

1

t

1

2

⇒t

1

=

a

1

2x

=

gsinθ

2x

Case (2) When there is friction,

From newton's second law, F=ma

⇒mgsinθ−μmgcosθ=ma

2

⇒a

2

=gsinθ−μgcosθ

Now, as body starts from rest so initial velocity (u)=0 m/s.

Let, body travels 'x' distance in t

2

time,

So from equation of motion,

x=ut+ 21 at 2

⇒x= 21 a 2t 22⇒t 2 = a 1

2x= gsinθ−μgcosθ2x

It is given that t

2=2t1

So,

gsinθ−μgcosθ

2x =2gsinθ2x

Now, substituting θ=45 and solving above equation we get,

1−μ1=2μ= 43=0.75

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