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The simple pendulum of length 40 cm is t...

The simple pendulum of length 40 cm is taken inside a deep mine. Assume for the time being that the mine is 1600 km deep. Calculate the time period of the pendulum there. Radius of the earth =6400 km.

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The correct Answer is:
A, D
Length of the pendulum =40 cm =0.4cm
let acceleration due to gravity be g at the depth of 1600 km
`:. g=g(1-d/r)`
`=9.8(1-1600/6400)`
`-9.8(1-1/4)`
`=9.8xx(3/4)=7.35ms^-2`
:. Time period
`T=2pisqrt(l/(g_delta))`
` =2pi sqrt(0.4/7.35)`
`2pixxsqrt0.054`
`=2pixx0.23`
`2xx3.14xx0.23`
`=1.465~~1.47sec`
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