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JEE Main Physics Class 11 System of Particles and Rotational Motion Part 1 Questions
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© examsnet.com
Question : 39
Total: 100
A thin
rod
M
N
,
free to rotate in the vertical plane about the fixed end
N
,
is held horizontal. When the end
M
is released the speed of this end, when the rod makes an angle
α
with the horizontal, will be proportional to: (see figure)
[Online April 15, 2018]
√
cos
α
cos
α
sin
α
√
sin
α
Validate
Solution:
When the rod makes an angle
α
Displacement of centre of
mass
=
l
2
cos
α
m
g
l
2
cos
α
=
l
2
I
ω
2
m
g
l
2
cos
α
=
m
l
2
6
ω
2
(
∵
M.I. of thin uniform rod about an axis passing through its centre of mass and perpendicular to the rod
I
=
m
l
2
12
)
⇒
ω
=
√
3
g
cos
α
l
Speed of end
=
ω
×
l
=
√
3
g
cos
α
l
i.e., Speed of end,
ω
∝
√
cos
α
© examsnet.com
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