Properties Of Solids And Liquids Question 276

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 $

therefore $ 2g\times 9=3gh $ \ h = 6 cm.



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