Maximum height reached by an object projected perpendicular to the surface of the earth with a speed equal to $50\%$ of the escape velocity from earth surface is - ( $R =$ Radius of Earth)
$\frac {R}{2}$
$\frac {16R}{9}$
$\frac {R}{3}$
$\frac {R}{8}$
The period of a satellite, in a circular orbit near an equatorial plane, will not depend on
A spherical part of radius $R/2$ is excavated from the asteroid of mass $M$ as shown in the figure. The gravitational acceleration at a point on the surface of the asteroid just above the excavation is
If the radius of the earth were shrink by $1\%$ and its mass remaining the same, the acceleration due to gravity on the earth's surface would
The change in the value of $g$ at a height $h$ above the surface of the earth is the same as at a depth $d$ below the surface of earth. When both $d$ and $h$ are much smaller than the radius of earth, then which one of the following is correct ?
The height at which the weight of a body becomes $\frac{1}{9} ^{th}$ its weight on the surface of earth (radius of earth is $R$)