A student is performing the experiment of resonance Column. The diameter of the column tube is 4 cm. The frequency of the tuning fork is 512 Hz. The air temperature is 38^oC in which the speed of sound is 336 m/s. The zero of the meter scale coincides with the top end of the Resonance Column tube. When the first resonance occurs, the reading of the water level in the column is

Two moles of ideal helium gas are in a rubber balloon at 30^oC. The balloon is fully expandable and can be assumed to require no energy in its expansion. The temperature of the gas in the balloon is slowly changed to 35^oC. The amount of heat required in raising the temperature is nearly (take R = 8.31 J/mol.K)

A thin uniform cylindrical shell, closed at both ends, is partially filled with water. It is floating vertically in water in half-submerged state. If $${\rho _c}$$ is the relative density of the material of the shell with respect to water, then the correct statement is that the shell is

Two spherical planets P and Q have the same uniform density r, masses M_P and M_Q and surface areas A and 4A respectively. A spherical planet R also has uniform density r and its mass is (M_P + M_Q). The escape velocities from the planets P, Q and R are V_P, V_Q and V_R, respectively. Then