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A simple pendulum with a bob of mass 40g...

A simple pendulum with a bob of mass 40g and charge `+2mu C` makes 20 oscillation in 44 s. A vertical electric field magnitude `4.2xx10^(4) NC^(-1)` pointing downward is applied. The time taken by the pendulum to make 15 oscillation in the electric field is (acceleration due to gravity `=10 ms^(-2)`)

A

30 s

B

60 s

C

90 s

D

15 s

Text Solution

Verified by Experts

The correct Answer is:
A
Mass, `m=40 g =0.04 kg, q=2xx10^(-6)C`
Now, `" "ma=qE`
`rArr a=(a)/(m) E`
`=(2xx10^(-6))/(0.04) xx4.2xx10^(4)m//s^(2)`
`=21 m//s^(2)` (downward)
So, effective acceleration on bob,
`a_(e)=a+g=121 m//s^(2)`
In the presence of electric field.
`T.=2pi sqrt((l)/(a_(e)))=2pi sqrt((l)/(121))`
`(T)/(T.) =sqrt((121)/(10)) =(11)/(10)rArrT. =(10)/(11) T`
Given, `" "T=(44)/(20) rArr T. =(10)/(11)xx(44)/(20) =2s`
So, time taken in 15 oscillations
`=2xx15=30s`
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