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A simple pendulam has time period T(1) w...

A simple pendulam has time period `T_(1)` when on the earth's surface and `T_(2)` when taken to a height `R` above the earth's surface where `R` is the radius of the earth. The value of `(T_(2))/(T_(1))` is-

A

`1`

B

`sqrt(2)`

C

`4`

D

`2`

Text Solution

Verified by Experts

The correct Answer is:
D
We know that `T_(1)=2pisqrt(l//g)` and `T_(2)=2pisqrt(l//g')`
`:. (T_(2))/(T_(1)=sqrt(g/g')`………..i
Also `g=(GM)/(R^(2))`
`:. g'=(GM)/((2R)^(2))=(GM)/(4RL)`
`:. g/(g')=4implies(T_(2))/(T_(1))=2`
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