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A ball whose density is 0.4 xx 10^3 kg//...

A ball whose density is `0.4 xx 10^3 kg//m^3` falls into water from a height of 9 cm. To what depth does the ball sink ?

A

9 cm

B

6 cm

C

4.5 cm

D

2.25 cm

Text Solution

Verified by Experts

The correct Answer is:
B
Velocity of ball just before entering the surface of water
`= sqrt(2gh) = sqrt(2xx980xx9 )` cm/s.
This velocity is retarded by the upthrust acting on the ball due to water. The retardation
` = ("net force")/("mass") = ( Vrho_g -vsigma_g)/(V_rho)=((rho-sigma)/(rho))`
`implies g = ((0.4-1)/(0.4))g = -3/2 g`
Hence, depth of penetration of ball into water is given by
`0^2 -2 xx 980 xx 9 = 2 (-3/2) xx 980 xxh`
`:. h = 6 cm`
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