If the distance between centres of earth and moon is $D$ and the mass of earth is $81\, times$ the mass of moon, then at what distance from centre of earth the gravitational force will be zero
$\frac{D}{2}$
$\frac{{2D}}{3}$
$\frac{{4D}}{3}$
$\frac{{9D}}{10}$
The period of a satellite, in a circular orbit near an equatorial plane, will not depend on
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 small ball of mass $'m'$ is released at a height $'R'$ above the Earth surface, as shown in the figure. If the maximum depth of the ball to which it goes is $R/2$ inside the Earth through a narrow grove before coming to rest momentarily. The grove, contain an ideal spring of spring constant $K$ and natural length $R,$ the value of $K$ is ( $R$ is radius of Earth and $M$ mass of Earth)
The height at which the weight of a body becomes $1/16^{th}$, its weight on the surface of earth (radius $R$), is
In a certain region of space, the gravitational field is given by $-k/r$ , where $r$ is the distance and $k$ is a constant. If the gravitational potential at $r = r_0$ be $V_0$ , then what is the expression for the gravitational potential $(V)$ ?