If the radius of earth shrinks by $2 \%$ while its mass remains same. The acceleration due to gravity on the earth's surface will approximately.

Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth $d=\frac{R}{2}$ from the surface of earth, if its werght on the surface of earth is $200\,N$, will be $...........\,N$ ( $Given R =$ Radrus of earth)

As we go from the equator to the poles, the value of $g$

Assuming the earth to be a sphere of uniform mass density, how much would a body weigh (in $N$) half way down to the centre of the earth if it weighed $250\; N$ on the surface?

A star of mass $M$ and radius $R$ is made up of gases. The average gravitational pressure compressing the star due to gravitational pull of the gases making up the star depends on $R$ as

$R$ is the radius of the earth and $\omega $ is its angular velocity and ${g_p}$ is the value of $g$ at the poles. The effective value of $g$ at the latitude $\lambda = 60^\circ $ will be equal to