$A$ body weighs $45 \ N$ on the surface of the earth. The gravitational force on a body due to the earth at a height equal to half the radius of the earth will be: (in $N$)

Considering Earth to be a sphere of radius $R$ having uniform density $\rho$,the value of acceleration due to gravity $g$ in terms of $R$,$\rho$,and $G$ is:

At a height $R$ above the earth's surface,the gravitational acceleration is ($R$ = radius of earth,$g$ = acceleration due to gravity on earth's surface).

The depth at which acceleration due to gravity becomes $\frac{g}{2n}$ is ($R=$ radius of earth,$g=$ acceleration due to gravity on earth's surface,$n$ is an integer).

$A$ spherical part of radius $R/2$ is excavated from an asteroid of mass $M$ and radius $R$ as shown in the figure. The gravitational acceleration at a point on the surface of the asteroid just above the excavation is

If the radius of the Earth contracts by $0.1 \%$,with its mass remaining the same,then the weight of a body at the Earth's surface will increase by ..............$\%$