The pressure and density of a diatomic gas $$\left(\gamma=\frac{7}{5}\right)$$ changes adiabatically from $$(\mathrm{P}, \rho)$$ to $$\left(\mathrm{P}^{\prime}, \rho^{\prime}\right)$$. If $$\frac{\rho^{\prime}}{\rho}=32$$ then $$\frac{\mathrm{P}^{\prime}}{\mathrm{P}}$$ should be

A source of sound is moving towards a stationary observer with $$\left(\frac{1}{10}\right)^{\text {th }}$$ the of the speed of sound. The ratio of apparent to real frequency is

If $$\mathrm{E}_{\mathrm{a}}$$ and $$\mathrm{E}_{\mathrm{q}}$$ represent the electric field intensity due to a short dipole at a point on its axial line and on the equatorial line at the same distance '$$r$$' from the centre of the dipole, then

In potentiometer experiment, the balancing length is $$8 \mathrm{~m}$$ when two cells $$E_1$$ and $$E_2$$ are joined in series. When two cells are connected in opposition the balancing length is $$4 \mathrm{~m}$$. The ratio of the e.m.f. of the two cells $$\left(\frac{E_1}{E_2}\right)$$ is