Gravitational Field Due to a Solid Sphere

Q.

Mass density of a solid sphere is ρ. Radius of the sphere is R. The gravitational field at distance r from the centre of the sphere inside it is

1. 

2. 

3. 

4. 

Q.

A solid sphere of radius $R$ gravitationally attracts a particle placed at $3R$ from its centre with a force $F_1$. Now a spherical cavity of radius $\frac{R}{2}$ is made in the sphere (as shown in figure) and the force becomes $F_2$. The value of $F_1:F_2$ is:

1. $41:50$

2. $36:25$

3. $50:41$

4. $25:36$

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

1. True
2. False

Q. In the figure shown, a block $A$ moving with velocity $20\text{m/s}$ on a horizontal surface collides with another identical block $B$, initially at rest. The coefficient of restitution is $0.5$. Neglect friction everywhere. The distance between the blocks, $5\text{sec}$ after the collision takes place is

1. $50\text{m}$
2. $125\text{m}$
3. $100\text{m}$
4. $150\text{m}$

Q.

The magnitude of the gravitational force at distance $r_1$ and $r_2$ from the centre of a uniform sphere of radius R and mass M are $F_1$ and $F_2$ respectively. Then,

1. 

2. 

3. 

4. 

Q.

Two spheres each of mass 70 kg are 0.14 m apart. Find the force of attraction between them.

Given $G=6.67\times {10}^{-11}N{m}^{2}k{g}^{-2}$.

Q. A uniform solid sphere of mass $m$ and radius $r$ is surrounded symmetrically by a uniform thin spherical shell of radius $2r$ and mass $m$. Choose the correct statement

1. The gravitational field at a distance of $2.5r$ from the centre is $\frac{8}{25}\frac{Gm}{r^2}$
2. The gravitational field between the sphere and spherical shell is uniform.
3. The gravitational field at a distance of $1.5r$ from the centre is $\frac{2}{9}\frac{Gm}{r^2}$
4. The gravitational field at a distance of $1.5r$ from the centre is zero.

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.

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 ball of mass $m$ moving at a speed $v$ makes a head on collision with an identical ball at rest. The kinetic energy of balls after the collision is ${\frac{3}{4}}^{\text{th}}$ of the original. If $e$ is the coefficient of restitution. Then:

1. After collision, ball which was initially at rest starts moving with velocity $\frac{1+\frac{1}{\sqrt{2}}}{2}v$
2. After collision, ball which was initially moving, has velocity $\frac{1-\frac{1}{\sqrt{2}}}{2}v$
3. $e=\frac{1}{\sqrt{2}}$
4. $e=\frac{1}{2}$

Q. A spherical solid ball of a 1$kg$ mass and radius $3cm$ is rotating about an axis passing through its centre with an angular velocity of $50radian/s$. The kinetic energy of rotation is (in J)

1. $4500$
   
2. $90$
   
3. $910$
   
4. $\frac{9}{20}$
   

Q. A uniform thin rod of mass $m$ and length $R$ is placed normally on surface of earth as shown. The mass of earth is $M$ and its radius is $R$. Then the magnitude of gravitational force exerted by earth on the rod is :

1. $\frac{GMm}{4R^2}$
2. $\frac{GMm}{2R^2}$
3. $\frac{4GMm}{9R^2}$
4. $\frac{GMm}{8R^2}$

Q.

Mass density of a solid sphere is ρ. Radius of the sphere is R. The gravitational field at distance r from the centre of the sphere inside it is

1. $\frac{4\rho G\pi r}{3}$

2. $\frac{4\rho G{r}^2}{3}$

3. $\frac{4\rho G{R}^3}{3r^2}$

4. $\frac{\rho G{R}^3}{\pi r}$

Q. A body P strikes head-on with another body Q of mass that is 'p' times that of body P and moving with a velocity that is $\frac{1}{q}$ of the velocity of body P. If the body P comes to rest, the coefficient of restitution is

1. $\frac{p+q}{(p-q)}$
2. $\frac{p-q}{q(p-1)}$
3. $\frac{p-q}{p(q-1)}$
4. $\frac{p+q}{p(q-1)}$