The gravitational potential at a point above the surface of earth is $-5.12 \times 10^7 \mathrm{~J} / \mathrm{kg}$ and the acceleration due to gravity at that point is $6.4 \mathrm{~m} / \mathrm{s}^2$. Assume that the mean radius of earth to be $6400 \mathrm{~km}$. The height of this point above the earth's surface is :

The mass and diameter of a planet are twice those of earth. What will be the period of oscillation of a pendulum on this planet if it is a seconds pendulum on earth ?

As we go from the equator to the poles, the value of $g$

A body weight $500 \,N$ on the surface of the earth. How much would it weigh half way below the surface of the earth ....... $N$

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

If the earth rotates faster than its present speed, the weight of an object will