Problem No$.1$: A $4$ kg ball moving with a velocity of $10$ m$/$s collides with a $16$ kg ball moving with a velocity of $4$ m$/$s $($i$)$ in the same direction, $($ii$)$ in the opposite direction. Calculate the velocity of the balls in each case if they coalesce $($stick together$)$ on impact, and the loss of kinetic energy resulting from the impact. $[$Hint: conservation of linear momentum$](25)$ Problem No$.2$: An object of mass $10$ kg is whirled round a horizontal circle of radius $4$ m by a revolving string inclined to the vertical. If the uniform speed of the object is $5$ m$/$s$,$ calculate $($i$)$ the tension in the string, $($ii$)$ the angle of inclination of the strong to the vertical. $[$Hint: circular motion$](25)$ Problem No$.3$: A bullet of mass $10$ g is fired from a gun of mass $1$ kg with a velocity of $100$ m$/$s$.$ Calculate the ratio of the kinetic energy of the bullet and the gun. $[$Hint: conservation of linear momentum$](25)$ Problem No$.4$: A cyclist while negotiating a circular path with speed $20$ m$/$s is found to bend an angle by $30$o with vertical. $($a$)$ What is the radius of the circular path? $($b$)$ Derive the formula you used to calculate the radius of circular path. $[$Hint: circular motion$](25)$