The r.m.s. speed of hydrogen at S.T.P. is '$u$' $\text{m/s}$. If the gas is heated at constant pressure till its volume becomes three times, the final temperature of the gas and the r.m.s. speed are respectively

An ideal gas is heated from $27^\circ\text{C}$ to $627^\circ\text{C}$ at constant pressure. If initial volume of gas is $4\ \text{m}^3$, then the new volume of the gas will be

All the springs in fig (a), (b) and (c) are identical, each one having force constant K. Mass m is attached to each system. If $T_a$, $T_b$ and $T_c$ are the periodic time of oscillations of the three systems in fig (a), (b) and (c) respectively, then

A particle is performing simple harmonic motion about $x = 0$ with an amplitude '$a$' and periodic time T. The speed of the particle at $x = \dfrac{a}{3}$ will be