Two identical discs of same radius R are rotating about their axes in opposite directions with the same constant angular speed $$\omega $$. The discs are in the same horizontal plane. At time t = 0, the points P and Q are facing each other as shown in the figure. The relative speed between the two points P and Q is v_r. In one time period (T) of rotation of the discs, v_r as a function of time is best represented by

Six point charges are kept at the vertices of a regular hexagon of side $$L$$ and center $$O,$$ as shown in the figure. Given that $$K = {1 \over {4\pi {\varepsilon _0}}}{q \over {{L^2}}},$$ which of the following statement(s) is (are) correct ?

In the given circuit, a charge of $$+80$$ $$\mu C$$ is given to the upper plate of the $$4$$ $$\mu F$$ capacitor. Then in the steady state, the charge on the upper plate of the $$3$$ $$\mu F$$ capacitor is

A student is performing the experiment of resonance Column. The diameter of the column tube is 4 cm. The frequency of the tuning fork is 512 Hz. The air temperature is 38^oC in which the speed of sound is 336 m/s. The zero of the meter scale coincides with the top end of the Resonance Column tube. When the first resonance occurs, the reading of the water level in the column is

Two moles of ideal helium gas are in a rubber balloon at 30^oC. The balloon is fully expandable and can be assumed to require no energy in its expansion. The temperature of the gas in the balloon is slowly changed to 35^oC. The amount of heat required in raising the temperature is nearly (take R = 8.31 J/mol.K)

A thin uniform cylindrical shell, closed at both ends, is partially filled with water. It is floating vertically in water in half-submerged state. If $${\rho _c}$$ is the relative density of the material of the shell with respect to water, then the correct statement is that the shell is

Two spherical planets P and Q have the same uniform density r, masses M_P and M_Q and surface areas A and 4A respectively. A spherical planet R also has uniform density r and its mass is (M_P + M_Q). The escape velocities from the planets P, Q and R are V_P, V_Q and V_R, respectively. Then

The figure shows a system consisting of (i) a ring of outer radius 3R rolling clockwise without slipping on a horizontal surface with angular speed $$\omega $$ and (ii) an inner disc of radius 2R rotating anti-clockwise with angular speed $${\omega \over 2}$$. The ring and disc are separated by frictionless ball bearings. The point P on the inner disc is at a distance R from the origin, where OP makes an angle of $$30^\circ $$ with the horizontal. Then with respect to the horizontal surface,

Two solid cylinders P and Q of same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder P has most of its mass concentrated near its surface, while Q has most of its mass concentrated near the axis. Which statement(s) is(are) correct?

Consider a disc rotating in the horizontal plane with a constant angular speed $$\omega $$ about its centre O. The disc has a shaded region on one side of the diameter and an unshaded region on the other side as shown in the figure. When the disc is in the orientation as shown, two pebbles P and Q are simultaneously projected at an angle towards R. The velocity of projection is in the y - z plane and is same for both pebbles with respect to the disc. Assume that (i) they land back on the disc before the disc has completed $${1 \over 8}$$ rotation, (ii) their range is less than half the disc radius, and (iii) $$\omega $$ remains constant throughout. Then

A loop carrying current $$l$$ lies in the xy-plane as shown in the figure. The unit vector $$\widehat k$$ is coming out of the plane of the paper. The magnetic moment of the current loop is

An infinite long hollow conducting cylinder with inner radius R/2 and outer radius R carries a uniform current density along its length. The magnitude of the magnetic field, $$\left| {\overrightarrow B } \right|$$ as a function of the radial distance r from the axis is best represented by

Which of the following statements about the instantaneous axis (passing through the centre of mass) is correct?

Which of the following statements regarding the angular speed about the instantaneous axis (passing through the centre of mass) is correct?

What is the maximum energy of the anti-neutrino?

If the anti-neutrino had a mass of 3 eV/c² (where c is the speed of light) instead of zero mass, what should be the range of the kinetic energy, K, of the electron?

For light incident from air on a meta-material, the appropriate ray diagram is

Choose the correct statement.

In the given circuit, the AC source has $$\omega$$ = 100 rad/s. Considering the inductor and capacitor to be ideal, the correct choice(s) is(are)

A current carrying infinitely long wire is kept along the diameter of a circular wire loop, without touching it, the correct statement(s) is(are)