A geostationary satellite is orbiting the earth at a height of $6\, R$ from the earth’s surface ($R$ is the earth’s radius ). What is the period of rotation of another satellite at a height of $2.5\, R$ from the earth’s surface
$6\sqrt 2 \,hours$
$10\, hours$
$\frac{{5\sqrt 5 }}{{\sqrt 3 }}\,hours$
none of the above
The kinetic energy needed to project a body of mass $m$ from the earth's surface (radius $R$) to infinity is
A satellite moving with velocity $v$ in a force free space collects stationary interplanetary dust at a rate of $\frac{{dM}}{{dt}} = \alpha v$ where $M$ is the mass (of satellite + dust) at that instant . The instantaneous acceleration of the satellite 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)
An object is taken to height $2 R$ above the surface of earth, the increase in potential energy is $[R$ is radius of earth]
A satellite of mass $m$ is in a circular orbit of radius $2R_E$ about the earth. The energy required to transfer it to a circular orbit of radius $4R_E$ is (where $M_E$ and $R_E$ is the mass and radius of the earth respectively)