Which of the following statements are true about acceleration due to gravity?
$(a)\, 'g'$ decreases in moving away from the centre if $r > R$
$(b)\, 'g'$ decreases in moving away from the centre if $r < R$
$(c)\, 'g'$ is zero at the centre of earth 
$(d)\, 'g'$ decreases if earth stops rotating on its axis

A box weighs $196 \;\mathrm{N}$ on a spring balance at the north pole. Its weight recorded on the same balance if it is shifted to the equator is close to ....... $N$

(Take $\mathrm{g}=10\; \mathrm{ms}^{-2}$ at the north pole and the radius of the earth $=6400\; \mathrm{km}$)

The moon's radius is $1/4$ that of the earth and its mass is $1/80$ times that of the earth. If $g$ represents the acceleration due to gravity on the surface of the earth, that on the surface of the moon is

The value of g on the earth's surface is $980\,cm/{\sec ^2}$. Its value at a height of $64 \,km$ from the earth's surface is ........ $cm/{\sec ^2}$

(Radius of the earth $R = 6400$ kilometers) 

At the surface of a certain planet, acceleration due to gravity is one-quarter of that on earth. If a brass ball is transported to this planet, then which one of the following statements is not correct

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.

Assertion $A:$ A pendulum clock when taken to Mount Everest becomes fast.

Reason $R:$ The value of $g$ (acceleration due to gravity) is less at Mount Everest than its value on the surface of earth.

In the light of the above statements, choose the most appropriate answer from the options given below