N moles of a diatomic gas in a cylinder are at a temperature T. Heat is supplied to the cylinder such that the temperature remains constant but n moles of the diatomic gas get converted into monoatomic gas. What is the change in the total kinetic energy of the gas ?

A block of mass 0.1 kg is connected to an elastic spring of spring constant 640 Nm⁻¹ and oscillates in a damping medium of damping constant 10⁻² kg s⁻¹ . The system dissipates its energy gradually. The time taken for its mechanical energy of vibration to drop to half of its initial value, is closest to :

A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by

y(x, t) = 0.5 sin $$\left( {{{5\pi } \over 4}x} \right)\,$$ cos(200 $$\pi $$t).

What is the speed of the travelling wave moving in the positive x direction ?

(x and t are in meter and second, respectively.)

A uniform wire of length 1 and radius r has a resistance of 100 $$\Omega $$. It is recast into a wire of radius $${r \over 2}.$$ The resistance of new wire will be :