A wave $$y=a$$ $$\sin \left( {\omega t - kx} \right)$$ on a string meets with another wave producing a node at $$x=0.$$ Then the equation of the unknown wave is

On moving a charge of $$20$$ coulomb by $$2$$ $$cm,$$ $$2$$ $$J$$ of work is done, then the potential differences between the points is

length of a string tied to two rigid supports is $$40$$ $$cm$$. Maximum length (wavelength in $$cm$$) of a stationary wave produced on it is

A cylinder of height $$20$$ $$m$$ is completely filled with water. The velocity of efflux of water (in $$m{s^{ - 1}}$$) through a small hole on the side wall of the cylinder near its bottom is