A particle performs simple harmonic motion with amplitude $$A.$$ Its speed is trebled at the instant that it is at a distance $${{2A} \over 3}$$ from equilibrium position. The new amplitude of the motion is:

A uniform string of length $$20$$ $$m$$ is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the supports is :
(take $${\,\,g = 10m{s^{ - 2}}}$$ )

A pipe open at both ends has a fundamental frequency $$f$$ in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now :

The region between two concentric spheres of radii $$'a'$$ and $$'b',$$ respectively (see figure), have volume charge density $$\rho = {A \over r},$$ where $$A$$ is a constant and $$r$$ is the distance from the center. A such that the electric field in the region between the spheres will be constant, is :