A person of 80 kg mass is standing on the rim of a circular platform of mass 200 kg rotating about its axis at 5 revolutions per minute (rpm). The person now starts moving towards the centre of the platform. What will be the rotational speed (in rpm) of the platform when the person reaches its centre _________.

A cricket ball of mass 0.15 kg is thrown vertically up by a bowling machine so that it rises to a maximum height of 20 m after leaving the machine. If the part pushing the ball applies a constant force F on the ball and moves horizontally a distance of 0.2 m while launching the ball, the value of F (in N) is (g = 10 ms^–2) ____.

A bakelite beaker has volume capacity of 500 cc at 30^oC. When it is partially filled with Vm volume (at 30^oC) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varied. If $$\gamma $$_(beaker) = 6 × 10^{–6 o}C^–1 and $$\gamma $$_(mercury) = 1.5 × 10^{–4 o}C^–1, where $$\gamma $$ is the coefficient of volume expansion, then V_m (in cc) is close to ____.

Consider a gas of triatomic molecules. The molecules are assumed to be triangular and made of massless rigid rods whose vertices are occupied by atoms. The internal energy of a mole of the gas at temperature T is :