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 ?

Two tubes of radii r₁ and r₂, and lengths l₁ and l₂ , respectively, are connected in series and a liquid flows through each of them in stream line conditions. P₁ and P₂ are pressure differences across the two tubes.

If P₂ is 4P₁ and l₂ is $${{{1_1}} \over 4}$$, then the radius r₂ will be equal to :

A steel rail of length 5 m and area of cross section 40cm² is prevented from expanding along its length while the temperature rises by 10^oC. If coefficient of linear expansion and Young’s modulus of steel are 1.2×10⁻⁵ K⁻¹ and 2×10¹¹ Nm⁻² respectively, the force developed in the rail is approximately :

A car is standing 200 m behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has acceleration 2 m/s² and the car has acceleration 4 m/s² . The car will catch up with the bus after a time of :