An insulated chamber at a height `h` above the earth's surface and maintained at `30^(@)C` has a clock fitted with an uncompensated pendulum. The maker of the clock for the chamber mistakenly design it to maintain correct time at `20^(@)C` at that height. it is found that if the chamber were brought to earth's surface the clock in it would click correct time at `30^(@)C`. the coefficient of linear expansion of the material of pendulum is (earth's radius is R)

Options

A. `(trianglel)/(10l)`
B. `(5R)/(h)`
C. `(h)/(5R)`
D. `(h)/(20R)`

Explanation

Clock is designed to indicate correct time at `20^(@)C` at height `h` it will idicate correct time at `30^(@)C` on the ground if in this case the time period is same as the earlier
`therefore2pisqrt((L)/(g_(h)))=2pisqrt((L')/(g_(s)))`
Here `L'=L(1+alpha10),g_(S)=(GM)/(R^(2))` and `g_(h)=(GM)/((R+h)^(2))implies(L)/(g_(n))=(L')/(g_(S))`
`impliesL(R+h)^(2)=L(1+alpha10)^(2)implies1+(h)/(R)=(1+alpha10)^(1//2)`
`implies1+(h)/(R)=1+5alpha` (by binomial expansion) `impliesalpha=(h)/(5R)`