The percentage decrease in the weight of a rocket,when taken to a height of $32 \ km$ above the surface of the Earth,will be $.....\%$
(Radius of Earth $= 6400 \ km$)

$T$ is the time period of a simple pendulum on the Earth's surface. Its time period becomes $xT$ when taken to a height $R$ (equal to the Earth's radius) above the Earth's surface. Then,the value of $x$ will be:

Acceleration due to gravity at the surface of a planet is equal to that at the surface of the Earth,and its density is $1.5$ times that of the Earth. If the radius of the Earth is $R$,the radius of the planet is:

If the earth were to cease rotating about its own axis,the increase in the value of $g$ in the $C.G.S.$ system at a place of latitude of $45^{\circ}$ will be ........ $cm/sec^{2}$.

State the values of $g$ and $G$ at the center of the Earth. Identify which of $g$ and $G$ is a vector and which is a scalar.

If the mass of the Earth decreases by $25 \%$ and its radius increases by $50 \%$,then the acceleration due to gravity at its surface decreases by nearly ......... $\%$