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Test Index
Work, Power and Energy Part 2
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Section:
Physics
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© examsnet.com
Question : 8
Total: 42
A bead of mass '
m
' slides without friction on the wall of a vertical circular hoop of radius '
R
' as shown in figure. The bead moves under the combined action of gravity and a massless spring (
k
) attached to the bottom of the hoop. The equilibrium length of the spring is '
R
'. If the bead is released from top of the hoop with (negligible) zero initial speed, velocity of bead, when the length of spring becomes '
R
', would be (spring constant is '
k
',
g
is acceleration due to gravity)
[28 Jan 2025 Shift 1]
√
2
R
g
+
‌
4
k
R
2
m
√
2
R
g
+
‌
k
R
2
m
√
3
R
g
+
‌
k
R
2
m
2
√
g
R
+
‌
k
R
2
m
Validate
Solution:
👈: Video Solution
Work done by gravity
=
m
g
(
2
R
−
R
‌
cos
‌
60
∘
)
=
‌
3
m
g
R
2
Work done by spring
=
−
‌
1
2
k
(
0
2
−
R
2
)
=
‌
1
2
k
R
2
Net work = change in kinetic energy
i.e.
‌
3
m
g
R
2
+
‌
k
R
2
2
=
‌
1
2
m
v
2
or
‌
‌
v
2
=
3
g
R
+
‌
k
R
2
m
or
‌
‌
v
=
√
3
g
R
+
‌
k
R
2
m
© examsnet.com
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