Magnitude of magnetic field (in SI units) at the centre of a hexagonal shape coil of side 10 cm, 50 turns and carrying current I (Ampere) in units of $${{{\mu _0}I} \over \pi }$$ is :

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 :

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 ____.

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) ____.