Physics

A plastic circular disc of radius 10cm is placed on a thin oil film of thickness 2mm, spread over a flat horizontal surface. The torque (N-m) required to spin the disc about its central vertical axis with a constant angular velocity 8 rad/sec is (coefficient of viscosity of oil is 1.0 kg/m-s) (take p = 3.14)

A proton and an $\alpha$ -particle both initially at rest are accelerated in a region of electric potential difference V and gravity free space. The proton is projected with gained kinetic energy against a uniform constant electric field and comes to momentary rest after travelling a distance $S_0$ . If the $\alpha$ -particle is also projected with gained kinetic energy against same electric field, it will come to momentary rest after travelling through:

The molar specific heat C_v of a diatomic gas is (5/2)R when we treat its molecules to be rigid having no vibrations. But this assumption is not always valid especially at high temperatures. In that case, molecules are treated as non-rigid having vibrational energy also. C_v for diatomic gas with non-rigid gas molecules will be:

Two infinite line charges having linear charge density λ₁ and λ₂ are placed along the x and y axis respectively. The electric field at a point (x₁, y₁) in the first quadrant is inclined at an angle of 60° with the x-axis. Then which of the following relations is correct.

The minimum and maximum distance of a satellite from the centre of the earth are 2R and 4R, respectively, where R is the radius of earth and M is the mass of earth. The radius of curvature at the point of maximum distance is

A satellite is moving around a planet of radius R in a circular orbit of radius r. The speed of the satellite is v. Find the acceleration due to gravity on the surface of the planet.

Assuming the sun to be a spherical body (e = 1) of radius R at a temperature of T K, evaluate the total radiant power, incident on Earth having radius r₀, at a distance r from the Sun, where r₀ is the radius of the earth and $\sigma$  is Stefan's constant.

Magnetic field exists in the region between lines PQ and RS as shown in the figure. A particle having charge to mass ratio of a enters the magnetic field as shown in the figure with a speed v. Lines PQ and RS are parallel to each other. Find the value of d such that the charged particle exits the magnetic field region with velocity perpendicular to line RS.

The absolute temperature of air in a region linearly increases from $T_1$ to $T_2$  in a space of width d. The time taken by the sound wave to travel in this region is (The velocity of sound at 273 k is v ):

An inverted cone is rotating about its vertical axis. A particle is kept on the inner surface of cone and it is at rest relative to the cone at a height of 0.4 m above its vertex. The coefficient of friction between the surface of cone and the particle is 0.6 and the apex angle of cone is 90°. The maximum angular velocity of revolution of the cone can be: (take g = 10/s²)