A particle of mass $M$ is placed at the centre of a uniform spherical shell of mass $2M$ and radius $R$. The gravitational potential on the surface of the shell is
$-\frac{GM}{R}$
$-\frac{3GM}{R}$
$-\frac{2GM}{R}$
Zero
$Assertion$ : The escape speed does not depend on the direction in which the projectile is fired.
$Reason$ : Attaining the escape speed is easier if a projectile is fired in the direction the launch site is moving as the earth rotates about its axis.
At what height above the earth's surface is the value of $'g'$ is same as in a $200\, km$ deep mine ........ $km$
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
A planet is revolving ground the sun in an elliptical orbit. Its closest distance from the sun is $r_{min}$, the farthest distance from the sun is $r_{max}$. If the orbital angular velocity of the planet when it is the nearest to the sun is $\omega $, then the orbital angular velocity at the point when it is at the farthest distance from the sun is
The orbital velocity of an artificial satellite in a circular orbit very close to earth is $v$. The velocity of a geo-stationary satellite orbiting in circular orbit at an altitude of $3R$ from earth's surface will be