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IIT JEE Advanced 2012 Paper 2
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© examsnet.com
Question : 19
Total: 60
Two solid cylinders P and Q of same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder P has most of its mass concentrated near its surface, while Q has most of its mass concentrated near the axis. Which statement(s) is(are) correct?
Both cylinders P and Q reach the ground at the same time.
Cylinder P has larger linear acceleration than cylinder Q.
Both cylinders reach the ground with same translational kinetic energy.
Cylinder Q reaches the ground with larger angular speed.
Validate
Solution:
Acceleration is expressed as
a =
M
g
s
i
n
θ
M
+
(
1
R
2
)
Hence, the acceleration of cylinders P and Q, respectively, are given by
a
P
=
M
g
s
i
n
θ
M
+
(
M
R
2
∕
R
2
)
~
g
2
a
Q
= g sin θ (as
I
Q
~ 0)
Therefore,
ω
p
=
√
2
(
g
2
)
l
R
=
√
g
l
R
ω
Q
=
√
2
g
l
R
Hence,
ω
Q
>
ω
P
.
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