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. `(h)/(R_(e))`
B. `(h)/(5R_(e))`
C. `(5R_(e))/(h)`
D. `(R_(e))/(h)`

Answer

B

Explanation

Variation of acceleration due to gravity with altitude
`g_(h) = g(1 - (2h)/(R_(e)))`
`Deltag = (2hg)/(R_(e))`
Variation of `l` with temperature `= Deltal`
`T_(h) = 2pisqrt((1)/(g - Deltag)) = 2pisqrt((l)/(g))(1 - (Deltag)/(g))^(1//2) = T(1 + (Deltag)/(2g))`
`T_(0) = 2pi sqrt((1 +Deltal)/(g)) = T(1 + (Deltal))/(l)`
The clock shows correct time if `T_(h) = T_(theta)`
`(Deltal)/(2I) = (Deltag)/(2g)` Linear expansity `= (Deltal)/(10l) = (Deltag)/(10g) = (2h)/(10R_(e)) = (h)/(5R_(e))`