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)

827-841

  • A

    $\frac {3GMm}{R^3}$

  • B

    $\frac {6GMm}{R^3}$

  • C

    $\frac {9GMm}{R^3}$

  • D

    $\frac {7GMm}{R^3}$

Similar Questions

A body of mass $m$ falls from a height $R$ above the surface of the earth, where $R$ is the radius of the earth. What is the velocity attained by the body on reaching the ground? (Acceleration due to gravity on the surface of the earth is $g$)

The two planets have radii $r_1$ and $r_2$ and their densities $p_1$ and $p_2$ respectively. The ratio of acceleration due to gravity on them will be

Escape velocity at the surface of earth is $11.2\,km/sec$ . If radius of planet is double that of earth but mean density same as that of earth then the escape velocity will be ........ $km/sec$

The magnitudes of gravitational field at distances $r_1$ and $r_2$ from the centre of a uniform sphere of radius $R$ and mass $M$ are $F_1$ and $F_2$ respectively. Then-

If the distance between the centres of Earth and Moon is $D$ and mass of Earth is $81\, times$ that of Moon. At what distance from the centre of Earth gravitational field will be zero?