If both the mass and the radius of the earth decrease by $1\%$,the value of the acceleration due to gravity will

State whether the following statements are true or false:
$(a)$ $G$ is a vector quantity.
$(b)$ The relation $g = \frac{GM}{r^2}$ holds well for all celestial bodies.
$(c)$ If the Earth suddenly stops rotating,the value of acceleration due to gravity at the equator will decrease.

$A$ simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is $4 \ m$,then the time period of small oscillations will be . . . . . . $s$. [Take $g = \pi^2 \ ms^{-2}$]

Suppose the earth stopped rotating. Then,the weight of a body will

Two spherical planets $A$ and $B$ have the same mass,but their densities are in a ratio $8:1$. For these planets,the ratio of acceleration due to gravity at the surface of $A$ to its value at the surface of $B$ is:

If the density of a small planet is the same as that of the Earth,while the radius of the planet is $0.2$ times that of the Earth,the gravitational acceleration on the surface of that planet is .......... $g$.