Question

If two balls each of mass $0.06kg$ moving in opposite directions with a speed of $4m/s$ collide and rebound with the same speed, then the impulse imparted to each ball due to the other is

• A. $0.48kgm/s$
• B. $0.24kgm/s$
• C. $0.81kgm/s$
• D. zero

Answer 1

The correct option is A

$0.48kgm/s$

Step 1: Given Data

Velocity before the collision $v_i=4m/s$

Velocity after the collision $v_f=-4m/s$

Given that mass of each ball $=0.06kg$

Velocity of collision $m=4m/s$

Step 2: Impulse

If $F$ is the force imparted and $∆t$ is the short time interval, then impulse is given as

$I=F∆t$

From Newton's second law of motion, we know that,

$F=\frac{∆p}{∆t}$

where $∆p$ is the change in momentum of the body.

$\therefore I=∆p$

Hence, an impulse is equal to the change in momentum of a body.

Step 3: Calculate the Impulse

$\therefore I=∆p$

$=m{v}_i-m{v}_f$

Upon substituting the values we get, $v_f=finalvelocitywouldbenegativeasitisrebound.$

$I=0.06\times 4-0.06\left(-4\right)$

$=0.24-\left(-0.24\right)$

$=0.24+0.24$

$=0.48kgm/s$

Hence, the correct answer is option (A).