$R$ is the radius of the earth and $\omega $ is its angular velocity and ${g_p}$ is the value of $g$ at the poles. The effective value of $g$ at the latitude $\lambda = 60^\circ $ will be equal to

If mass of earth decreases by $25 \%$ and its radius increases by $50 \%$, then acceleration due to gravity at its surface decreases by nearly ……… $\%$

Imagine a new planet having the same density as that of earth but it is $3$ times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is $g$ and that on the surface of the new planet is $g^{\prime}$, then

A simple pendulum has a time period ${T_1}$ when on the earth’s surface and ${T_2}$ when taken to a height $R$ above the earth’s surface, where $R$ is the radius of the earth. The value of ${T_2}/{T_1}$ is

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