A small ball with charge q is suspended by a non-conducting thread of length I at the point O on the non-
conducting wall, forming a small angle a with the vertical. A point charge q is fixed at O. Then the thread
with the ball was deviated through a small angle (B>a) and set free. Assuming the collision of the ball
against the wall to be perfectly elastic and neglecting, the effect of charge induced on the wall, select the
correct option. Take T as period of oscillation and g as acceleration due to gravity
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Explanation:
ANSWER
The motion of the string can be represented as an angular displacement from the mean position,given as: θ=βsin(ωt)
Time taken from displacement from mean position to β and back to mean position=t
1
=
2
T
where T is the time period of the oscillation without the wall barrier.
Thus t
1
=
2
1
×2π
g
L
=π
g
L
Time taken to displace from mean position to α can be found by:
α=βsin(ωt)
⟹t=
ω
1
sin
−1
β
α
=
g
L
sin
−1
β
α
Thus time taken to displace from mean position to α and back to mean position = t
2
=2
g
L
sin
−1
β
α
Thus the time period of the oscillation = t
1
+t
2
=
g
L
[π+2sin
−1
β
α
]
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