The magnitude of gravitational potential energy of a body at a distance `r` from the centre of earth is u. Its weight at a distance 2r from the centre of earth is

Options

A. `4xx10^(-3)N`
B. `4xx10^(-2)N`
C. `8xx10^(-2)N`
D. `8xx10^(-3)N`

Answer

B

Explanation

Gravitational P.E. of the rocket `U_(1)=-(GMm)/(r_(1))`
`therefore GM=|(U_(1)r_(1))/(m)|`
weight of a distance `r_(1)=w_(1)=mg_(1)=m(GM)/(r_(1)^(2))`
`because g_(1)=(GM)/(r_(1)^(2))`
and `w_(2)=mg_(2)=m[(GM)/(r_(2)^(2))]`
`=m[(U_(1)r_(1))/(m)]xx(1)/(r_(2)^(2))=(U_(1)r_(1))/(r_(2)^(2))`
`therefore w_(2)=(4xx10^(9)xx10^(7))/(10^(9)xx10^(9))=4xx10^(-2)N`