A cup of tea cools from $80\,^oC$ to $60\,^oC$ in one minute. The ambient temperature is $30\,^oC$. In cooling from $60\,^oC$ to $50\,^oC$. It will take ……. $\sec$

Gravitational force is required for

Certain quantity of water cools from $70\,^oC$ to $60\,^oC$ in the first $5\, minutes$ and  to $54\,^oC$ in the next $5\, minutes$. The temperature of the surroundings is……… $^oC$

The intensity of radiation emitted by the Sun has its maximum value at a wavelength of $510\,\, nm$ and that emitted by the North Star has the maximum value at $350\,\, nm$. If these stars behave like black bodies then the ratio of the surface temperature of the Sun and the North Star is

Two identical conducting rods are first connected independently to two vessels, one containing water at $100^o\ C$ and the other containing ice at $0^o\  C$. In the second case, the rods are joined end to end and connected to the same vessels. Let $q_1$ and $q_2\  g/s$ be the rate of melting of ice in the two cases respectively. The ratio $q_2/q_1$ is