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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

9cm

B

6cm

C

4.5 cm

D

2.25cm

Text Solution

Verified by Experts

The correct Answer is:
B
Velocity of body before centering the surface of water ` = sqrt(2gh) = sqrt(2 xx 980 xx 9) ` cm/s
This velocity is retarded due to upthrust experienced by water. The retardation is , `a = (F_("net"))/(m) = (W - B)/(m)`
` = (V rho g - V sigma g)/(V rho) = ((rho - sigma)/(rho))g`
`rho ` = density of body , `sigma = ` density of water
` = ((0.4 - 1)/(0.4)) g = (3)/(-2) g `
Depth of penetration h is given by
`0^2 - 2 xx 980 xx 9 = 2 ((-3)/(2) ) xx 980 h, h = 6cm`
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