Question

$10,000$ small balls, each weighing $1g$ strike one square $cm$ of area per second with a velocity of $100m{s}^{-1}$ 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

$2\times {10}^{7}N{m}^{-2}$

Step 1. Given data.

No of balls $=10000$

mass of each ball $=1g={10}^{-3}Kg$

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

Velocity $=100m{s}^{-1}$

Step 2. Calculating pressure.

Pressure $=\frac{Force}{area}=\frac{ma}{A}$

$$\begin{gathered} =\frac{[noofballs\times massofeachball\times changeinvelocityperunittime]}{Area} \\ =\frac{10000\times {10}^{-3}\times (v–(–v\left)\right)}{{10}^{-4}} \end{gathered}$$

As the ball rebound with the same velocity hence $v_2=–v$

$$\begin{gathered} =\frac{10000\times {10}^{-3}\times 2\times 100}{{10}^{-4}} \\ =2\times {10}^{7}N/m^2 \end{gathered}$$

Hence, the correct option is (D).