Gravitational Potential

Q. Find the gravitational force of attraction between the ring and sphere as shown in the diagram, where the plane of the ring is perpendicular to the line joining the centres. If $\sqrt{8}$$R$ is the distance between the centres of a ring (of mass $m$) and a sphere (of mass $M$) where both have equal radius $R$.

1. $\frac{\sqrt{8}}{9}\frac{GmM}{R}$
2. $\frac{1}{3\sqrt{8}}\frac{GmM}{R^2}$
3. $\sqrt{2}$ $\frac{GmM}{R^2}$
4. $\frac{\sqrt{8}}{27}\frac{GmM}{R^2}$

Q.

In some region, the gravitational field is zero. The gravitational potential in this region

1. Must be variable

2. Must be constant

3. Cannot be zero

4. Must be zero

Q. A solid sphere of uniform density and radius $4$ units is located with its centre at the origin O of coordinates. Two spheres of equal radii $1$ unit with their centres at $A(–2,0,0)$ and $(2,0,0)$ respectively are taken out of the solid leaving behind spherical cavities as shown in figure

1. The gravitational potential is the same at all points on the circle $y^2+z^2=4$
2. The gravitational force due to this object at the origin is zero
3. The gravitational force at the point $B(2,0,0)$ is zero
4. The gravitational potential is the same at all points of the circle $y^2+z^2=36$

Q.

The potential at the surface of a planet of mass M and radius R is assumed to be zero. Choose the most appropriate option

1. The potential at infinity is $\frac{GM}{R}$

2. The potential at the center of planet is $-\frac{GM}{R}$

3. Both (a) and (b) are correct

4. Both (a) and (b) are wrong

Q.

A solid sphere of uniform density and radius 4 units is located with its centre at the origin O of coordinates. Two spheres of equal radii 1 unit with their centres at A(- 2, 0, 0) and B(2, 0, 0) respectively are taken out of the solid leaving behind spherical cavities as shown in figure. Then,

1. The gravitational force due to this object at the origin is zero

2. The gravitational force at the point B (2, 0, 0) is zero

3. The gravitational potential is the same at all points of the circle $y^2+z^2=36$

4. The gravitational potential is the same at all points of the circle $y^2+z^2=4$

Q.

Two masses 90 kg and 160 kg are at a distance 5 m apart. Compute the magnitude of intensity of the gravitational field at a point distance 3m from the 90 kg and 4m from the 160 kg mass. G=6.67 $\times$ ${10}^{-11}$SI units..

1. 9.43 $\times$ ${10}^{-10}$ N $k{g}^{-1}$

2. 4.43 $\times$ ${10}^{-10}$ N $k{g}^{-1}$

3. 6.43 $\times$ ${10}^{-10}$ N $k{g}^{-1}$

4. 0.43 $\times$ ${10}^{-10}$ N $k{g}^{-1}$