The mass and diameter of a planet have twice the value of the corresponding parameters of earth. Acceleration due to gravity on the surface of the planet is ........ $m/{\sec ^2}$.

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?

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

A mass falls from a helght $h$ and its time of fall $t$ is recorded in terms of time period $T$ of a simple pendulum. On the surface of earth it is found that $t =2 T$. The entre setup is taken on the surface of another planet whose mass is half of that of earth and radius the same. Same experiment is repeated and corresponding times noted as $t'$ and $T'$.

At  ..... $km$ height from the surface of earth the gravitation potential and the value of $g$ are  $-5.4 \times 10^7\, J kg^{-1}$ and $6.0\,m s^{-2}$ respectively . Take the radius of earth as $6400\, km$.

A weight is suspended from the ceiling of a lift by a spring balance. When the lift is stationary the spring balance reads $W$. If the lift suddenly falls freely under gravity, the reading on the spring balance will be