Mechanical Properties of Fluids — Physics STD 12 Science — Question

Find the ratio of the de Broglie wavelengths of an electron and a proton when both are moving with the (a) same speed, (b) same energy and (c) same momentum? State which of the two will have the longer wavelength in each case?

Explain the use of a sonometer to verify
(i) the law of length
(ii) the law of tension
(iii) the law of linear density.

State an expression for the moment of inertia of a solid uniform disc, rotating about an axis passing through its centre, perpendicular to its plane. Hence derive an expression for the moment of inertia and radius of gyration:
(i) about a tangent in the plane of the disc, and (ii) about a tangent perpendicular to the plane of the disc

Derive an expression for the electric potential at a point due to a short electric dipole. Hence, write the expression for the electric potential at a point
(i) on the dipole axis (ii) on the dipole equator.
OR
Derive an expression for the electric potential at a point due to an electric dipole.

Derive an expression for the maximum safe speed for a vehicle on a circular horizontal road without toppling/overturning/rollover.

Derive an expression for the excess pressure inside a soap bubble.
OR
Derive Laplace's law for spherical membrane of a bubble due to surface tension.

Explain the concept of free path of a gas molecule. Define free path and mean free path. State the expression for mean free path.

With the help of a neat diagram, explain the working of the npn transistor?