Fluid Mechanics Viscosity Question 195
Question: A ball whose density is 0.4 × 103 kg/m3 falls into water from a height of 9 cm . To what depth does the ball sink
Options:
A)9 cm
B)6 cm
C)4.5 cm
D)2.25 cm
Show Answer
Answer:
Correct Answer: B
Solution:
The velocity of ball before entering the water surface$ v=\sqrt{2gh}=\sqrt{2g\times 9} $ When ball enters into water, due to upthrust of water the velocity of ball decreases (or retarded)The retardation, a = $ \frac{\text{apparent weight}}{\text{mass of ball}} $ $ \frac{=V(\rho -\sigma )g}{V\rho } $ $ =\left( \frac{\rho -\sigma }{\rho } \right)g $ $ =\left( \frac{0.4-1}{0.4} \right)\times g $ $ =-\frac{3}{2}g $ If h be the depth upto which ball sink, then,$ 0-v^{2}=2\times \left( -\frac{3}{2}g \right)\times h $ Þ $ 2g\times 9=3gh $ \ h = 6 cm.
BETA
