What should be the angular speed of earth, so that body lying on equator may appear weightlessness $ (g = 10\,m/{s^2},\,\,R = 6400\,km)$
$\frac{1}{{800}}rad/s$
$\frac{1}{{400}}rad/s$
$\frac{1}{{600}}rad/s$
$\frac{1}{{100}}rad/s$
Three identical bodies of equal mass $M$ each are moving along a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each body is
Two identical spheres are placed in contact with each other. The force of gravitation between the spheres will be proportional to ($R =$ radius of each sphere)
Two stars of masses $m_1$ and $m_2$ are parts of a binary star system. The radii of their orbits are $r_1$ and $r_2$ respectively, measured from the centre of mass of the system. The magnitude of gravitational force $m_1$ exerts on $m_2$ is
A particle of mass $M$ is situated at the centre of a spherical shell of same mass and radius $a$. The gravitational potential at a point situated at $\frac{a}{2}$ distance from the centre, will be
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