Gravitational Potential of a Ring

Q. A ring shaped object of radius $R$ contains mass $M$ distributed non-uniformly. Which of the following graphs correctly represents the variation of gravitational potential at a point on the axis of ring?
(Assume that ring is in YZ plane with origin as centre)

1. 
2. 
3. 
4. 

Q. A thin uniform annular disc of mass $M$ has an outer radius $4R$ and an inner radius $3R$ as shown in the figure. The work required to take a unit mass from point $\text{P}$ on its axis to infinity is

1. $\frac{2GM}{R}(4\sqrt{2}-5)$
2. $\frac{GM}{4R}$
3. $\frac{4GM}{7R}(4\sqrt{2}-5)$
4. $\frac{2GM}{7R}(4\sqrt{2}-5)$

Q. A thin uniform annular disc of mass $M$ has an outer radius $4R$ and an inner radius $3R$ as shown in the figure. The work required to take a unit mass from point $\text{P}$ on its axis to infinity is

1. $\frac{2GM}{R}(4\sqrt{2}-5)$
2. $\frac{2GM}{7R}(4\sqrt{2}-5)$
3. $\frac{GM}{4R}$
4. $\frac{4GM}{7R}(4\sqrt{2}-5)$

Q. Two identical thin rings each of radius $R$ are coaxially placed at a separation of $R$. If the rings have a uniform mass distribution and masses $m_1$ and $m_2$ respectively, then the work done in moving a mass $m$ from centre of the ring having mass $m_1$ to center of the other ring is

1. $\frac{Gm(2-\sqrt{2})(m_2-m_1)}{2R}$
2. $\frac{Gm(2-\sqrt{2})(m_1-m_2)}{2R}$
3. $0$
4. $\frac{Gm(2-\sqrt{2})(m_1+m_2)}{2R}$
   

Q. Two rings having masses $M$ and $2M$, respectively, having the same radius are placed coaxially as shown in the figure. If the mass distribution on both the rings is non-uniform, then the gravitational potential at point $P$ is

1. Zero
2. $-\frac{GM}{R}[\frac{1}{\sqrt{2}}-\frac{2}{\sqrt{5}}]$
3. $-\frac{GM}{R}[1+\frac{1}{\sqrt{2}}]$
4. $-\frac{GM}{R}[\frac{1}{\sqrt{2}}+\frac{2}{\sqrt{5}}]$