If a man at the equator would weigh $(3/5)^{th}$ of his weight, the angular speed of the earth is
$\sqrt {\frac{2}{5}\,\frac{g}{R}} $
$\sqrt {\frac{g}{R}} $
$\sqrt {\frac{R}{g}} $
$\sqrt {\frac{2}{5}\,\frac{R}{g}} $
Weight of a body of mass m decreases by $1\%$ when it is raised to height $h$ above the earth’s surface. If the body is taken to a depth h in a mine, change in its weight is
Two planets have the same average density but their radii are ${R_1}$ and ${R_2}$. If acceleration due to gravity on these planets be ${g_1}$ and ${g_2}$ respectively, then
A body weighs $700 \,gm$ wt on the surface of the earth. How much will it weigh on the surface of a planet whose mass is $\frac{1}{7}$ and radius is half that of the earth ........ $gm\, wt$
A ball is launched from the top of Mt. Everest which is at elevation of $9000 \,m$. The ball moves in circular orbit around earth. Acceleration due to gravity near the earth's surface is $g$. The magnitude of the ball's acceleration while in orbit is
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