Gravitational Field Due to a Solid Sphere

Q. The acceleration due to gravity at the surface of the planet is directly proportional to its density.

1. True
2. False

Q. A uniform sphere of mass $M$ and radius $R$ is surrounded by a concentric spherical shell of same mass but radius $2R.$ A point mass $m$ is kept at a distance $x(>R)$ in the region bounded by spheres as shown in the figure. The net gravitational force on the particle is

1. 
   $\frac{G(M+m)}{x^2}$
2. 
   $\frac{GMm}{x^2}$
3. 
   $\frac{GMmx}{R^3}$
4. zero

Q. A spherically symmetric gravitational system of particles has a mass density $\rho =\{\begin{array}{c}{\rho }_0\text{for}r\le R\\ 0\text{for}r>R\end{array}$
where ${\rho }_0$ is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed $V$ as a function of distance $r(0<r<\infty )$ from the centre of the system is represented by

1. 
2. 
3. 
4. 

Q. A solid sphere of uniform density and radius $R$ applies a gravitational force of attraction equal to $F_1$ on a particle placed at a distance $3R$ from the centre of the sphere. A spherical cavity of radius $\frac{R}{2}$ is now made in the sphere as shown in the figure. The sphere with cavity now applies a gravitational force $F_2$ on the same particle. The ratio $\frac{F_2}{F_1}$ is:

1. $\frac{9}{50}$
2. $\frac{41}{50}$
3. $\frac{3}{25}$
4. $\frac{22}{25}$

Q. A planet has mass $\frac{1}{10}$ of that of earth, while radius is $\frac{1}{3}$ that of earth. If a person can throw a stone on earth surface to a height of $90\text{m}$, then he will be able to throw the stone on that planet to a height (in m)Assume that velocity of projection remains same on earth and planet.