Let $$\omega_1, \omega_2$$ and $$\omega_3$$ be the angular speed of the second hand, minute hand and hour hand of a smoothly running analog clock, respectively. If $$x_1, x_2$$ and $$x_3$$ are their respective angular distances in 1 minute then the factor which remains constant $$(k)$$ is
The magnetic moment of an iron bar is $$M$$. It is now bent in such a way that it forms an arc section of a circle subtending an angle of $$60^{\circ}$$ at the centre. The magnetic moment of this arc section is
The given circuit shows a uniform straight wire $$A B$$ of $$40 \mathrm{~cm}$$ length fixed at both ends. In order to get zero reading in the galvanometer $$G$$, the free end of $$J$$ is to be placed from $$B$$ at:
According to the law of equipartition of energy, the number of vibrational modes of a polyatomic gas of constant $$\gamma=\frac{C_p}{C_v}$$ is ($$C_P$$ where $$C_V$$ are the specific heat capacities of the gas at constant pressure and constant volume, respectively):