The diagrams below show regions of equipotential. 
        
A positive charge is moved from \(A\) to \(B\) 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 \(\mathrm{(a)}.\)
3.	maximum work is required to move \(q\) in figure \(\mathrm{(b)}.\)
4.	maximum work is required to move \(q\) in figure \(\mathrm{(c)}.\)

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)

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. \(\dfrac{\sqrt5}{2\pi}\)
2. \(\dfrac{4\pi}{\sqrt5}\)
3. \(\dfrac{4\pi}{\sqrt3}\)
4. \(\dfrac{\sqrt5}{\pi}\)

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. \(\dfrac{I_0}{4}\)

2. \(\dfrac{I_0}{8}\)

3. \(\dfrac{I_0}{16}\)

4. \(\dfrac{I_0}{2}\)

The bulk modulus of a spherical object is \(B.\) If it is subjected to uniform pressure \(P,\) the fractional decrease in radius is:

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. \(1.41\times 10^{-8}~\text{T}\)

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. \(\frac{1}{2}I\left(\omega_1-\omega_2\right)^2\)