A ball with a speed of 9 m/s collides with another identical ball at rest. After the collision, the direction of each ball makes an angle of 30$$^\circ$$ with the original direction. The ratio of velocities of the balls after collision is x : y, where x is __________.

The centre of mass of solid hemisphere of radius 8 cm is x from the centre of the flat surface. Then value of x is __________.

Two bodies of the same mass are moving with the same speed, but in different directions in a plane. They have a completely inelastic collision and move together thereafter with a final speed which is half of their initial speed. The angle between the initial velocities of the two bodies (in degree) 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 :