Class 12th

Two uniform circular discs are rotating independently in the same direction around their common axis passing through their centres. The moment of inertia and angular velocity of the first disc are 0.1 kg–m² and 10 rads⁻¹ respectively while those for the second one are 0.2 kg–m² and 5 rads⁻¹ respectively. At some instant, they get stuck together and start rotating as a single system about their common axis with some angular speed. The kinetic energy of the combined system is:

A wire carrying current I is bent in the shape ABCDEFA as shown, where rectangles ABCDA and ADEFA are perpendicular to each other. If the sides of the rectangles are of lengths a and b, then the magnitude and direction of magnetic moment of the loop ABCDEFA is:

An inductance coil has a reactance of 100Ω. When an AC signal of frequency 1000 Hz is applied to the coil, the applied voltage leads the current by 45°. The self-inductance of the coil is:

The figure shows a region of length 'l' with a uniform magnetic field of 0.3 T in it and a proton entering the region with velocity 4 * 10⁵ ms⁻¹ making an angle 60° with the field. If the proton completes 10 revolution by the time it cross the region shown, 'l' is close to (mass of proton = 1.67 * 10⁻²⁷ kg, charge of the proton = 1.6 * 10⁻¹⁹C)

When the temperature of metal wire is increased from 0°C to 10°C, its length increases by 0.02%. The percentage change in its mass density will be close to: