Solveeit Logo
Login

Question

Question: At what height over the earth's pole, the free fall acceleration decreases by one percent (assume th...

At what height over the earth's pole, the free fall acceleration decreases by one percent (assume the radius of earth to be 6400 km)

A

32 km

B

80 km

C

1.253 km

D

64 km

Answer

32 km

Explanation

Solution

g∝GMr2g \propto \frac { G M } { r ^ { 2 } } ∴ g∝1r2g \propto \frac { 1 } { r ^ { 2 } } or r∝1gr \propto \frac { 1 } { \sqrt { g } }

If g decrease by one percent then r should be increase by 12%\frac { 1 } { 2 } \%i.e R = 12×100×6400=32 km\frac { 1 } { 2 \times 100 } \times 6400 = 32 \mathrm {~km}