A particle of mass m is moving along the x-axis with initial velocity $$u\widehat i$$. It collides elastically with a particle of mass 10 m at rest and then moves with half its initial kinetic energy (see figure). If $$\sin {\theta _1} = \sqrt n \sin {\theta _2}$$ then value of n is ________.

A square shaped hole of side l = $${a \over 2}$$ is carved out at a distance d = $${a \over 2}$$ from the centre ‘O’ of a uniform circular disk of radius a. If the distance of the centre of mass of the remaining portion form O is $$ - {a \over X}$$ , value of X (to the nearest integer) is :

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 ___________.