When an object is kept at a distance of 30 cm from a concave mirror, the image is formed at a distance of 10 cm from the mirror. If the object is moved with a speed of 9 cms^–1, the speed (in cms^–1) with which image moves at that instant is ____.

To raise the temperature of a certain mass of gas by 50^oC at a constant pressure, 160 calories of heat is required. When the same mass of gas is cooled by 100^oC at constant volume, 240 calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal)?

A block of mass 1.9 kg is at rest at the edge of a table, of height 1 m. A bullet of mass 0.1 kg collides with the block and sticks to it. If the velocity of the bullet is 20 m/s in the horizontal direction just before the collision then the kinetic energy just before the combined system strikes the floor, is [Take g = 10 m/s² . Assume there is no rotational motion and loss of energy after the collision is negligable.]

Concentric metallic hollow spheres of radii R and 4R hold charges Q₁ and Q₂ respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference V(R) – V(4R) is :