Air is pushed in a soap bubble to increase its radius from 'R' to '2R'. In this case, the pressure inside the bubble

The equation of wave is given by $$\mathrm{y}=10 \sin \left(\frac{2 \pi \mathrm{t}}{30}+\alpha\right)$$. If the displacement is $$5 \mathrm{~cm}$$ at $$\mathrm{t}=0$$, then the total phase at $$\mathrm{t}=7.5 \mathrm{~s}$$ will be

$$\left[\sin 30^{\circ}=\cos 60^{\circ}=\frac{1}{2}, \cos 30^{\circ}=\sin 60^{\circ}=\frac{\sqrt{3}}{2}\right] $$

A uniformly charged half ring of a radius ' $R$ ' has linear charge density '$$\sigma$$'. The electric potential at the centre of the half ring is ( $$\epsilon_0=$$ permittivity of free space)

A sonometer wire resonates with 4 antinodes between two bridges for a given tuning fork, when 1 kg mass is suspended from the wire. Using same fork, when mass M is suspended, the wire resonates producing 2 antinodes between the two bridges (distance between two bridges is as before). The value of M is