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.

Two identical ladders, each of mass M and length L are resting on the rough horizontal surface as shown in the figure. A block of mass $$m$$ hangs from P. If the system is in equilibrium, find the magnitude and the direction of frictional force at A and B.

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