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NEET Exam Model Paper 7
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© examsnet.com
Question : 7
Total: 180
Two point masses of 0.3 kg and 0.7 kg are fixed at the ends of a rod of length 1.4 m and of negligible mass.The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum, is located at a distance of
0.42 m from mass of 0.3 kg
0.70 m from mass of 0.7 kg
0.98 m from mass of 0.3 kg
0.98 m from mass of 0.7 kg
Validate
Solution:
Let the axis of rotation
Pass through O.
I
=
m
r
2
for point mass
∴
I
=
I
1
+
I
2
0.3
x
2
+
0.7
(
1.4
−
x
2
)
=
0.3
x
2
+
0.7
(
1.96
+
x
2
−
2.8
x
)
x
2
+
1.372
−
1.96
x
The work done for rotation of
The rod is stored as rotational kinetic energy,
1
3
I
ω
2
, of rod
Or
W
=
I
ω
2
2
=
1
2
(
x
2
+
1.372
−
1.96
x
)
ω
2
For work done to be minimum,
d
W
d
x
=
0
∴
d
d
x
(
x
2
+
1.372
−
1.96
x
)
ω
2
2
=
0
Or
2
x
+
0
−
1.96
=
0
Or
2
x
=
1.96
or
x
=
0.98
m
© examsnet.com
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