The temperature of a gas is $$-68^{\circ} \mathrm{C}$$. To what temperature should it be heated, so that the r.m.s. velocity of the molecules be doubled?

The displacement of a particle executing S.H.M. is $$x=\mathrm{a} \sin (\omega t-\phi)$$. Velocity of the particle at time $$\mathrm{t}=\frac{\phi}{\omega}$$ is $$\left(\cos 0^{\circ}=1\right)$$

A uniformly charged semicircular arc of radius '$$r$$' has linear charge density '$$\lambda$$'. The electric field at its centre is ( $$\varepsilon_0=$$ permittivity of free space)

A sphere, a cube and a thin circular plate all made of same material and having the same mass are heated to same temperature of $$200^{\circ} \mathrm{C}$$. When these are left in a room.