An unknown resistance X is to be determined using resistances R$$_1$$, R$$_2$$ or R$$_3$$. Their corresponding null points are A, B and C. Find which of the above will give the most accurate reading and why ?

A transverse harmonic disturbance is produced in a string. The maximum transverse velocity is 3 m/s and the maximum transverse acceleration is 90 m/s$$^2$$ . If the wave velocity is 20 m/s, then find the waveform.

A cylinder of mass m and radius R rolls down on an inclined plane of inclination $$\theta$$. Calculate the linear acceleration of axis of cylinder.

A long solenoid of radius a and number of turns per unit length $$n$$ is enclosed by cylindrical shell of radius R, thickness $$d$$ $$(d < < R)$$ and length L. A variable current $$\mathrm{I}=\mathrm{I}_{0} \sin \omega t$$ flows through the coil. If the resistivity of the material of cylindrical shell is $$\mathrm{P}$$, find the induced current in the shell.