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
$\frac{{GM}}{{{R^2}}}$
$\frac{{GM}}{{2{R^2}}}$
$\frac{{GM}}{{8{R^2}}}$
$\frac{{7GM}}{{8{R^2}}}$
Two spherical bodies of mass $M$ and $5M$ and radii $R$ and $2R$ respectively are released in free space with initial separation between their centres equal to $12\,R$. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is
Suppose the earth stopped rotating. Then, the weight a body will
A spherical planet far out in space has a mass ${M_0}$ and diameter ${D_0}$. A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity which is equal to
Suppose the gravitational force varies inversely as the $n^{th}$ power of the distance. Then, the time period of a planet in circular orbit of radius $R$ around the sun will be proportional to
Which of the following graph represents the variations of acceleration due to gravity $(g)$ with distance $r$ from the centre of earth?