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BITSAT 2018 Slot 2 Solved Paper
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© examsnet.com
Question : 23
Total: 150
An object takes
n
times as much time to slide down a
45
°
rough inclined plane as it takes to slide down a perfectly smooth
45
°
inclined plane. The coefficient of kinetic friction between the rough plane and the object is
n
2
−
1
1
−
1
n
2
n
2
+
1
1
+
1
n
2
Validate
Solution:
s
=
u
t
+
1
2
a
t
2
,
a
=
g
sin
θ
,
u
=
0
Then,
s
=
0
+
1
2
a
t
2
or
t
=
√
2
s
a
=
√
2
s
g
sin
θ
[for smooth plane
]
For the rough plane, the effective value of acceleration along the incline is
a
′
=
g
sin
θ
−
µ
k
g
cos
θ
and
t
′
=
√
2
s
a
=
√
2
s
g
sin
θ
−
µ
k
g
cos
θ
Now,
t
′
t
=
n
=
√
g
sin
θ
g
sin
θ
−
µ
k
g
cos
θ
=
√
sin
45
°
sin
45
°
−
µ
k
cos
45
°
=
√
1
1
−
µ
k
⇒
1
n
2
=
1
−
µ
k
⇒
µ
k
=
1
−
1
n
2
© examsnet.com
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