Assume that the acceleration due to gravity on the surface of the moon is $0.2$ times the acceleration due to gravity on the surface of the earth. If ${R_e}$ is the maximum range of a projectile on the earth’s surface, what is the maximum range on the surface of the moon for the same velocity of projection

The height at which the weight of the body become $\frac{1}{9}^{th}$. Its weight on the surface of earth (radius of earth $R$)

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

A planet has same density as that of earth and universal gravitational constant $G$ is twice that of earth, the ratio of acceleration due to gravity, is.

A planet of radius $R =\frac{1}{10} \times$ (radius of Earth) has the same mass density as Earth. Scientists dig a well of depth $\frac{R}{5}$ on it and lower a wire of the same length and of linear mass density $10^{-3} \ kgm ^{-1}$ into it. If the wire is not touching anywhere, the force applied at the top of the wire by a person holding it in place is (take the radius of Earth $=6 \times 10^6 \ m$ and the acceleration due to gravity on Earth is $10 \ ms ^{-2}$ )

If the acceleration due to gravity experienced by a point mass at a height $h$ above the surface of earth is same as that of the acceleration due to gravity at a depth a depth $\alpha$ h $\left(h \ll R_{e}\right)$ from the earth surface. The value of $\alpha$ will be$....$(use $R _{ e }=6400\,km$ )