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

The photoelectric threshold wavelength of silver is \(3250\times 10^{-10}~\text{m}.\) What will be the velocity of the electron ejected from a silver surface by the ultraviolet light of wavelength \(2536\times 10^{-10}~\text{m}?\) 
(Given \(h= 4.14\times 10^{-15}~\text{eVs}\)$$ and $\mathrm{}$\(c= 3\times 10^{8}~\text{m/s}\)${\mathrm{}}^{}$)
1. \(\approx 0.6\times 10^{6}~\text{m/s}\)
2. \(\approx 61\times 10^{3}~\text{m/s}\)
3. \(\approx 0.3\times 10^{6}~\text{m/s}\)
4. \(\approx 0.3\times 10^{5}~\text{m/s}\)

A \(250\) turn rectangular coil of length \(2.1\) cm and width \(1.25\) cm carries a current of \(85~\mu\text{A}\) and subjected to the magnetic field of strength \(0.85~\text{T}\). Work done for rotating the coil by \(180^\circ\) against the torque is:
1. \(4.55~\mu\text{J} \)
2. \(2.3~\mu\text{J} \)
3. \(1.15~\mu\text{J} \)
4. \(9.4~\mu\text{J} \)

The ratio of wavelengths of the last line of the Balmer series and the last line of the Lyman series is:
1. \(1\)
2. \(4\)
3. \(0.5\)
4. \(2\)

A Carnot engine having an efficiency of \(\frac{1}{10}\) as heat engine, is used as a refrigerator. If the work done on the system is \(10\) J, the amount of energy absorbed from the reservoir at a lower temperature is:
1. \(90\) J
2. \(99\) J
3. \(100\) J
4. \(1\) J

A gas mixture consists of \(2\) moles of \(\mathrm{O_2}\) and \(4\) moles of \(\mathrm{Ar}\) at temperature \(T.\) Neglecting all the vibrational modes, the total internal energy of the system is:

An arrangement of three parallel straight wires placed perpendicular to the plane of paper carrying the same current in the same direction is shown in the figure. The magnitude of force per unit length on the middle wire \(B\) is given by:
    
1. \(\dfrac{\mu_0i^2}{2\pi d}\)
2. \(\dfrac{2\mu_0i^2}{\pi d}\)
3. \(\dfrac{\sqrt{2}\mu_0i^2}{\pi d}\)
4. \(\dfrac{\mu_0i^2}{\sqrt{2}\pi d}\)

A \(U\text-\)tube with both ends open to the atmosphere is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a level of \(10~\text{mm}\) above the water level on the other side. Meanwhile, the water rises by \(65~\text{mm}\) from its original level (see diagram). The density of the oil is: 
                
1. \(425~\text{kg m}^{-3}\)
2. \(800~\text{kg m}^{-3}\)
3. \(928~\text{kg m}^{-3}\)
4. \(650~\text{kg m}^{-3}\)

Which of the following statements are correct? 

The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature \(T\) (kelvin) and mass \(m\), is: