Gravitational Potential of a Shell

Q. Inside a uniform spherical shell:
(a) the gravitational field is zero
(b) the gravitational potential is zero
(c) the gravitational field is same everywhere
(d) the gravitational potential is same everywhere
(e) all of the above
Choose the most appropriate answer from the options given below :

1. (a), (c) and (d) only
2. (e) only
3. (a), (b) and (c) only
4. (b), (c) and (d) only

Q. A uniform spherical shell gradually shrinks maintaining its shape. The gravitational potential at the centre

1. Increases
2. Decreases
3. Remains constant
4. Oscillates

Q. A spherical shell is cut into two pieces along a chord as shown in the figure. $P$ is a point on the plane of the chord. The gravitational field at $P$ due to the upper part is $I_1$ and that due to the lower part is $I_2$. What is the relation between them?

1. 
   $I_1>I_2$
2. 
   $I_1<I_2$
3. 
   $I_1=I_2$
4. 
   no definite relation

Q. The following figure shows two shells of masses $m_1$ and $m_2$. The shells are concentric. At which point, a particle of mass $m$ shall experience zero force?

1. $\text{A}$
2. $\text{B}$
3. $\text{C}$
4. $\text{D}$

Q. Intensity of gravitational field inside hollow uniform spherical shell

1. is zero at center but nonzero at other points.
2. is nonzero at all points.
3. is zero at all points because variables regims of shell attracts point mass in various directions, these forces cancel each other completely.
4. is non uniform & varies linearly.

Q. A cavity of radius $\frac{R}{2}$is made inside a solid sphere of radius $R$. The centre of the cavity is located at a distance $\frac{R}{2}$ from the centre of the sphere. The gravitational field intensity at a point $\text{P}$, as shown in the figure is:

[Here $g=\frac{GM}{R^2}$, where $M$ is the mass of the solid sphere without cavity]

1. $0$
2. $\frac{g}{4}$, towards Right
   
3. $\frac{g}{2}$, towards left
   
4. $\frac{g}{4}$, towards Right
   

Q. A uniform metal sphere of radius $a$ and mass $M$ is surrounded by a thin uniform spherical shell of equal mass and radius $4a$. The centre of the shell lies on the surface of the inner sphere. Find the gravitational field intensity at point ${\text{P}}_1$ lying on the same vertical line joining the two centers as shown in the figure.

1. $\frac{GM}{16a^2}$
   
2. $\frac{GM}{8a^2}$
3. $\frac{GM}{2a^2}$
4. $\frac{GM}{4a^2}$

Q. Intensity of gravitational field inside hollow uniform spherical shell

1. is zero at center but nonzero at other points.
2. is nonzero at all points.
3. is zero at all points because variables regims of shell attracts point mass in various directions, these forces cancel each other completely.
4. is non uniform & varies linearly.

Q. A hollow spherical shell is compressed to half of its radius, the gravitational potential at the centre.

1. decreases
2. increases
3. remains same
4. During the compression increases and then returns at the previous value.

Q. Intensity of gravitational field inside a hollow uniform spherical shell

1. is zero at centre but non-zero at other points.
2. is non-zero at all points.
3. is zero at all points because various region of shell attracts point mass in various directions, these forces cancel each other completely.
4. is non-uniform & varies linearly.

Q. A uniform spherical shell gradually shrinks maintaining its shape. The gravitational potential at the centre

1. Increases
2. Decreases
3. Remains constant
4. Oscillates

Q. Intensity of gravitational field inside a hollow uniform spherical shell

1. is zero at centre but non-zero at other points.
2. is non-zero at all points.
3. is zero at all points because various region of shell attracts point mass in various directions, these forces cancel each other completely.
4. is non-uniform & varies linearly.

Q. The following figure shows two shells of masses $m_1$ and $m_2$. The shells are concentric. At which point, a particle of mass $m$ shall experience zero force?

1. $\text{A}$
2. $\text{B}$
3. $\text{C}$
4. $\text{D}$

Q. A spherical shell is cut into two pieces along a chord as shown in the figure. $P$ is a point on the plane of the chord. The gravitational field at $P$ due to the upper part is $I_1$ and that due to the lower part is $I_2$. What is the relation between them?

1. 
   $I_1>I_2$
2. 
   $I_1<I_2$
3. 
   $I_1=I_2$
4. 
   no definite relation