If '$$l$$' is the length of the open pipe, '$$r$$' is the internal radius of the pipe and '$V$ ' is the velocity of sound in air then fundamental frequency of open pipe is

The angle of deviation produced by a thin prism when placed in air is '$$\delta_1$$' and that when immersed in water is '$$\delta_2$$'. The refractive index of glass and water are $$\frac{3}{2}$$ and $$\frac{4}{3}$$ respectively. The ratio $$\delta_1: \delta_2$$ is

A thin uniform rod of mass '$$m$$' and length '$$P$$' is suspended from one end which can oscillate in a vertical plane about the point of intersection. It is pulled to one side and then released. It passes through the equilibrium position with angular speed '$$\omega$$'. The kinetic energy while passing through mean position is

Magnetic field at the centre of the hydrogen atom due to motion of electron in $$\mathrm{n}^{\text {th }}$$ orbit is proportional to