Assuming the earth to be a sphere of uniform density,the acceleration due to gravity inside the earth at a distance of $r$ from the centre is proportional to

$A$ body weighs $49 \, N$ on a spring balance at the North Pole. What will be its weight recorded on the same weighing machine if it is shifted to the equator (in $, N$)? (Use $g = \frac{GM}{R^2} = 9.8 \, m/s^2$ and radius of the Earth,$R = 6400 \, km$.)

If the mass of the Sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude,which of the following is not correct?

Weight of a body decreases by $1.5 \%$ when it is raised to a height $h$ above the surface of the Earth. When the same body is taken to the same depth $h$ in a mine,its weight will show ........

If the earth suddenly shrinks (without changing mass) to half of its present radius,the acceleration due to gravity will be

The diameters of two planets are in the ratio $4:1$. Their mean densities have the ratio $1:2$. The ratio of gravitational acceleration on the surface of the planets will be: