Question

A ball of mass $2kg$ is connected to a string of length $1m$ and made to move in a horizontal circle on a smooth frictionless table with a constant speed of $2m/s$. The other end of the string is connected to a fixed peg on the table. Find the magnitude of the average impulse exerted by the string on the ball in half a revolution:

• A. $0$
• B. $8N-s$
• C. $4N-s$
• D. $2\sqrt{2}$ $N-s$

Answer 1

The correct option is B $8N-s$

Velocity of the ball at a particular point of the circular path $V_i=2m/s$
Velocity of the ball at its diametrical opposite point of the path $V_f=-2m/s$
Mass of ball $m=2kg$
Change in momentum of the ball $|\Delta P|=|m{V}_f-m{V}_i|$
$\therefore$ $|\Delta P|=\left(2\right)|-2-2|=8kgm/s$
Impulse $I=\Delta P=8N-s$