A piece of ice (heat capacity = 2100 J kg^{-1 o}C^-1 and latent heat = 3.36 $$ \times $$ 10⁵ J kg^-1 ) of mass m grams is at - 5 ^oC at atmospheric pressure. It is given 420 J of heat so that the ice starts melting. Finally when the ice-water mixture is in equilibrium, it is found that 1 gm of ice has melted. Assuming there is no other heat exchange in the process, the value of m is

Two spherical bodies A (radius 6 cm ) and B (radius 18 cm ) are at temperature T₁ and T₂, respectively. The maximum intensity in the emission spectrum of A is at 500 nm and in that of B is at 1500 nm. Considering them to be black bodies, what will be the ratio of the rate of total energy radiated by A to that of B?

A few electric field lines for a system of two charges $${Q_1}$$ and $${Q_2}$$ fixed at two different points on the $$x$$-axis are shown in the figure. These lines suggest that

A student uses a simple pendulum of exactly 1m length to determine g, the acceleration due to gravity. He uses a stop watch with the least count of 1 sec for this and records 40 seconds for 20 oscillations. For this observation, which of the following statement(s) is (are) true?