A body A, of mass m = 0.1 kg has an initial velocity of 3$$\widehat i$$ ms^-1 . It collides elastically with another body, B of the same mass which has an initial velocity of 5$$\widehat j$$ ms^-1. After collision, A moves with a velocity $$\overrightarrow v = 4\left( {\widehat i + \widehat j} \right)$$. The energy of B after collision is written as $${x \over {10}}$$. The value of x is ___________.

A point object in air is in front of the curved surface of a plano-convex lens. The radius of curvature of the curved surface is 30 cm and the refractive index of the lens material is 1.5, then the focal length of the lens (in cm) is ______.

A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP is 300 m/s, the frequency difference between the fundamental and second harmonic of this pipe is ________ Hz.

A particle is moving along the x-axis with its coordinate with the time 't' given be
x(t) = 10 + 8t – 3t². Another particle is moving the y-axis with its coordinate as a function of time given by y(t) = 5 – 8t³.
At t = 1s, the speed of the second particle as measured in the frame of the first particle is given as $$\sqrt v $$. Then v (in m/s) is ______.