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4-1.Newton's Laws of Motion
medium
$10^{-2}\; m^2$ આડછેદનું ક્ષેત્રફળ ધરાવતી એક નળીમાં $15\; m s^{-1}$ ની ઝડપે સમક્ષિતિજ વહન કરતા પાણીના પ્રવાહમાંથી પાણી બહાર ધસી આવીને નજીકની ઊર્ધ્વ દીવાલને અથડાય છે. પાણીની અસરથી દીવાલ પર લાગતું બળ કેટલું હશે ? પાણી પાછું ફેંકાતું $(rebound)$ નથી તેમ ધારો.
A$1500$
B$1125$
C$4500$
D$2250$
Solution
Speed of the water stream, $v=15 \,m / s$
Cross-sectional area of the tube, $A=10^{-2}\, m ^{2}$
Volume of water coming out from the pipe per second,
$V=A v=15 \times 10^{-2} \,m ^{3} / s$
Density of water, $\rho=10^{3}\, kg / m ^{3}$
Mass of water flowing out through the pipe per second $=\rho \times V=150 \,kg / s$
The water strikes the wall and does not rebound. Therefore, the force exerted by the water on the wall is given by Newton's second law of motion as:
$F=$ Rate of change of momentum $=\frac{\Delta P}{\Delta t}$ $=\frac{m v}{t}$
$=150 \times 15=2250\, N$
Cross-sectional area of the tube, $A=10^{-2}\, m ^{2}$
Volume of water coming out from the pipe per second,
$V=A v=15 \times 10^{-2} \,m ^{3} / s$
Density of water, $\rho=10^{3}\, kg / m ^{3}$
Mass of water flowing out through the pipe per second $=\rho \times V=150 \,kg / s$
The water strikes the wall and does not rebound. Therefore, the force exerted by the water on the wall is given by Newton's second law of motion as:
$F=$ Rate of change of momentum $=\frac{\Delta P}{\Delta t}$ $=\frac{m v}{t}$
$=150 \times 15=2250\, N$
Standard 11
Physics
