$A$ planet has double the mass of the earth. Its average density is equal to that of the earth. An object weighing $W$ on earth will weigh on that planet:

The radius of Earth is about $6400 \,km$ and that of Mars is $3200 \,km$,and the mass of the Earth is about $10$ times the mass of Mars. An object weighs $200 \,N$ on the surface of Earth. Then,its weight on the surface of Mars will be (in $\,N$)

The difference in the acceleration due to gravity at the pole and equator is ( $g=$ acceleration due to gravity,$R=$ radius of earth,$\theta=$ latitude,$\omega=$ angular velocity,$\cos 0^{\circ}=1, \cos 90^{\circ}=0$ ).

The value of gravitational acceleration $g'$ at a height $h$ above the earth's surface is $\frac{g}{4}$. Then,what is the value of $h$ in terms of the earth's radius $R$?

The value of $g$ at a particular point is $9.8\,m/s^2$. Suppose the Earth suddenly shrinks uniformly to half its present size without losing any mass. The value of $g$ at the same point (assuming that the distance of the point from the centre of the Earth does not shrink) will now be ......... $m/s^2$.

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 ..............$\%$