Question

$n$ balls each of mass $m$ impinge elastically each second on a surface with velocity $u$. The average force experienced by the surface will be

• A. $mnu$
• B. $2mnu$
• C. $4mnu$
• D. $mnu/2$

Answer 1

Answer: (B)

$2mnu$

• Elastically means the balls get bounced with $same$ speed i.e $u$
• so the change in momentum will be $P_2-P_1=-mu-mu=-2mu$
• so the momentum tranferred to the surface will be $-(-2mu)=2mu$
• thus the total momentum transferred by $n$ balls will be $2mnu$
• force $F=\frac{Momentum}{time}=\frac{2mnu}{1sec}=2mnu$