Question

If $n$ balls hit elastically and normally on a surface per unit time and all the balls are of mass $m$ moving with the same velocity $u$, then force on the surface is:

• A. $m\times u\times n$
• B. $2\times m\times u\times n$
• C. $\frac{1}{2}\times m{u}^{2}n$
• D. $m{u}^{2}n$

Answer 1

The correct option is B $2\times m\times u\times n$

Since the ball rebounds with same speed but in opposite direction.

So, change in linear momentum of one ball $\Delta P=P_f-P_i=mu-(-mu)=2mu$

Number of ball hitting the surface per second is $n$

So, total change in momentum in one second $\Delta P_T=n\times 2mu$

So, force acting on the surface $F=2mnu$