NEET Physics Gravitation Gravitational Field,Gravitational Potential MCQs

A binary star system consists of two stars of masses $M$ and $2M$ separated by a distance $d$. A small asteroid of mass $m$ is placed on the line joining the two stars at a distance $x$ from the star of mass $M$. If the net gravitational force on the asteroid is zero, what is the ratio $x/d$?

A spherical shell of uniform mass density $\rho$ and inner radius $R_1$ and outer radius $R_2$ exerts a gravitational force on a point mass $m$ located at a distance $r$ from the center. Which of the following expressions correctly represents the gravitational field strength experienced by the point mass when $R_1 < r < R_2$?

Two concentric spherical shells of mass $M_1$ and $M_2$ and radii $R_1$ and $R_2$ ($R_2 > R_1$) respectively, are placed in free space. The gravitational potential at a distance $r$ such that $R_1 < r < R_2$, from the center is:

A particle is projected vertically upwards from the surface of Earth with a speed equal to half the escape velocity. The maximum height reached by the particle, measured from the surface of Earth, is (R = radius of Earth):

A solid sphere of uniform density $\rho$ and radius $R$ has a concentric spherical cavity of radius $R/2$. The gravitational field at a distance $r = R/4$ from the center is:

A spherical shell of mass $M$ and radius $R$ has a small hole. A particle of mass $m$ is released from rest at a distance of $2R$ from the center of the shell. As the particle passes through the hole, its speed is $v_1$. Now, if the particle is released from rest at a distance of $\frac{3R}{2}$ inside the shell, its speed as it passes through the hole is $v_2$. What is the ratio $\frac{v_1}{v_2}$?

The gravitational field strength at a point is defined as:

The SI unit of gravitational potential is:

If the gravitational potential at a point is -10 J/kg, what does it signify?

The gravitational field is always directed: