Figure shows a ball having a charge \(q\) fixed at a point $\mathrm{A}$. Two identical balls having charges \(+q\) and \(–q\) and mass \(‘m’\) each are attached to the ends of a light rod of length $\mathrm{}$\(2 a\). The rod is free to rotate about a fixed axis perpendicular to the plane of the paper and passing through the mid-point of the rod. The system is released from the situation as shown in the figure. The angular velocity of the rod when the rod becomes horizontal will be:

         

1.	\(\frac{\sqrt{2}q}{3 \pi \varepsilon_0 {ma}^3} \)	2.	\(\frac{q}{\sqrt{3 \pi \varepsilon_0 {ma}^3 }}\)
3.	\(\frac{q}{\sqrt{6 \pi \varepsilon_0 {ma}^3 }} \)	4.	\(\frac{\sqrt{2} q}{4 \pi \varepsilon_0 m a^3} \)

A proton and an $\mathrm{\alpha }$-particle are at a distance r from each other. After letting them free if they move to infinity, the kinetic energy of the proton will be -

1.  $8{\mathrm{Ke}}^2/5\mathrm{r}$                           

2.  $2{\mathrm{Ke}}^2/5\mathrm{r}$

3.  $8{\mathrm{Ke}}^2/\mathrm{r}$                             

4.  ${\mathrm{Ke}}^2/5\mathrm{r}$

${10}^3$ small water drops, each of radius r and each carrying charge q, combine to form one bigger drop. The potential of a bigger drop as compared to that of a smaller drop will be.

1.  ${10}^5 \mathrm{V}$                     

2.  ${10}^3 \mathrm{V}$

3.  $10 \mathrm{V}$                       

4.  ${10}^2 \mathrm{V}$

The plates of a parallel plate capacitor have an area of $90 {\mathrm{cm}}^2$ each and are separated by $2.5 \mathrm{mm}$. The capacitor is charged by a 400 volt supply. How much electrostatic energy is stored by the capacitor?

1.  $2.55\times {10}^{-6} \mathrm{J}$                         

2.  $1.55\times {10}^{-6} \mathrm{J}$

3.  $8.15\times {10}^{-6} \mathrm{J}$                         

4.  $5.5\times {10}^{-6} \mathrm{J}$

An alpha particle with kinetic energy $10 \mathrm{MeV}$ is heading towards a stationary nucleus of atomic number $50$. Calculate the distance of closest approach.

1.  $1.4\times {10}^{-15} \mathrm{m}$                         

2.  $4\times {10}^{-15} \mathrm{m}$

3.  $14.4\times {10}^{-15} \mathrm{m}$                       

4.  $8\times {10}^{-15} \mathrm{m}$

Calculate the area of the plates of a one farad parallel plate capacitor if the separation between plates is $1 \mathrm{mm}$ and plates are in a vacuum.

1.  $18\times {10}^8 {\mathrm{m}}^2$                 

2.  $0.3\times {10}^8 {\mathrm{m}}^2$

3.  $1.3\times {10}^8 {\mathrm{m}}^2$               

4.  $1.13\times {10}^8 {\mathrm{m}}^2$

A solid conducting sphere of radius a having a charge $\mathrm{q}$ is surrounded by a concentric conducting spherical shell of inner radius $2\mathrm{a}$ and outer radius $3\mathrm{a}$ as shown in figure.

Find the amount of heat produced when switch is closed.

1. ${\mathrm{Kq}}^2/2\mathrm{a}$                         

2. ${\mathrm{Kq}}^2/3\mathrm{a}$

3. ${\mathrm{Kq}}^2/4\mathrm{a}$                         

4. ${\mathrm{Kq}}^2/6\mathrm{a}$

A parallel plate capacitor of area ‘A’ , plate separation ‘d’ is filled with two dielectrics as shown. What is the capacitance of the arrangement ?

1.  $\frac{3{\mathrm{K\epsilon }}_0\mathrm{A}}{4\mathrm{d}}$                             

2. $\frac{4{\mathrm{K\epsilon }}_0\mathrm{A}}{3\mathrm{d}}$

3. $\frac{\left(\mathrm{K}+1\right){\mathrm{\epsilon }}_0\mathrm{A}}{2\mathrm{d}}$                       

4.$\frac{\mathrm{K}\left(\mathrm{K}+3\right){\mathrm{\epsilon }}_0\mathrm{A}}{2\left(\mathrm{K}+1\right)\mathrm{d}}$

Assertion : A particle $\mathrm{A}$ of mass m and charge $\mathrm{Q}$ moves directly towards a fixed particle $\mathrm{B}$, which

                  has charge $\mathrm{Q}$. The speed of $\mathrm{A}$ is $\mathrm{v}$ when it is far away from $\mathrm{B}$. The minimum separation

                  between the particles is proportional to ${\mathrm{Q}}^2$.

Reason : Total energy remains conserved.

Assertion : Potential difference between two points lying in a uniform electric field may be equal

                  to zero.

Reason : Points of line normal to electric field is equipotential line.