The diagrams below show regions of equipotential. 
      
A positive charge is moved from \(\mathrm{A}\) to \(\mathrm{B}\) in each diagram. Choose the correct statement from the options given below:

1.	in all four cases, the work done is the same.
2.	minimum work is required to move \(q\) in figure (a).
3.	maximum work is required to move \(q\) in figure (b).
4.	maximum work is required to move \(q\) in figure (c).

Two astronauts are floating in gravitation-free space after having lost contact with their spaceship. The two will:

The \(x\) and \(y\) coordinates of the particle at any time are \(x=5 t-2 t^2\) and \({y}=10{t}\) respectively, where \(x\) and \(y\) are in meters and \(\mathrm{t}\) in seconds. The acceleration of the particle at \(\mathrm{t}=2\) s is:

One end of the string of length \(l\) is connected to a particle of mass \(m\) and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in a circle with speed \(v\), the net force on the particle (directed towards the center) will be: (\(T\) represents the tension in the string)
1. \(T+\frac{m v^2}{l}\)
2. \(T-\frac{m v^2}{l}\)
3. zero
4. \(T\)

A particle executes linear simple harmonic motion with amplitude of \(3~\text{cm}\). When the particle is at \(2~\text{cm}\) from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is:
1. \(\frac{\sqrt5}{2\pi}\)
2. \(\frac{4\pi}{\sqrt5}\)
3. \(\frac{4\pi}{\sqrt3}\)
4. \(\frac{\sqrt5}{\pi}\)

Two polaroids \(P_1\) and \(P_2\) are placed with their axis perpendicular to each other. Unpolarised light of intensity \(I_0\) is incident on \(P_1\). A third polaroid \(P_3\) is kept in between \(P_1\) and \(P_2\) such that its axis makes an angle \(45^\circ\) with that of \(P_1\). The intensity of transmitted light through \(P_2\) is:
1. \(\frac{I_0}{4}\)
2. \(\frac{I_0}{8}\)
3. \(\frac{I_0}{16}\)
4. \(\frac{I_0}{2}\)

The bulk modulus of a spherical object is \(B.\) If it is subjected to uniform pressure \(P,\) the fractional decrease in radius is:
1. \(\frac{B}{3P}\)
2. \(\frac{3P}{B}\)
3. \(\frac{P}{3B}\)
4. \(\frac{P}{B}\)

In an electromagnetic wave in free space, the root mean square value of the electric field is \(E_{\text{rms}} = 6~\text{V/m}\). The peak value of the magnetic field is:
1. \(2.83\times 10^{-8}~\text{T}\)
2. \(0.70\times 10^{-8}~\text{T}\)
3. \(4.23\times 10^{-8}~\text{T}\)
4. \(1.41\times 10^{-8}~\text{T}\)

A rope is wrapped around a hollow cylinder with a mass of \(3\) kg and a radius of \(40\) cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of \(30\) N?
1. \(0.25 ~\text{rad/s}^2 \)
2. \(25 ~\text{rad/s}^2 \)
3. \(5 ~\text{m/s}^2 \)
4. \(25 ~\text{m/s}^2 \)

Two discs of the same moment of inertia are rotating about their regular axis passing through centre and perpendicular to the plane of the disc with angular velocities \(\omega_1\) ${\mathrm{}}_{}$and \(\omega_2\). They are brought into contact face to face with their axis of rotation coinciding. The expression for loss of energy during this process is:
1. \(\frac{1}{4}I\left(\omega_1-\omega_2\right)^2\)
2. \(I\left(\omega_1-\omega_2\right)^2\)
3. \(\frac{1}{8}I\left(\omega_1-\omega_2\right)^2\)
4. \(\frac{1}{2}I\left(\omega_1-\omega_2\right)^2\)