Question

$10,000$ small balls, each weighing $1$gm, strike one square cm of area per second with a velocity $100$ m/s in a normal direction and rebound with the same velocity. The value of pressure on the surface will be.

• A. $2\times {10}^3$N$/m^2$
• B. $2\times {10}^5$N$/m^2$
• C. ${10}^7$N$/m^2$
• D. $2\times {10}^7$N$/m^2$

Answer 1

The correct option is D $2\times {10}^7$N$/m^2$

Change in momentum of one ball $\Delta P=mv-(-mv)=2mv$

Change in momentum of 10000 balls in one second $\Delta P_t=10000\times 2mv=20000mv$

$⟹\Delta P_t=20000\times \left({10}^{-3}\right)\times 100=2000kgm/s$

Force acting $F=\frac{\Delta P_t}{\Delta t}=\frac{2000}{1}=2000N$

Area $A=1c{m}^2={10}^{-4}{m}^2$

Pressure $P=\frac{F}{A}=\frac{2000}{{10}^{-4}}=2\times {10}^{7}N{m}^{-2}$

Option D is correct.