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A wooden cube (density 0.5 gm/c c) of si...

A wooden cube (density 0.5 gm/c c) of side 10 cm floating in water kept in a cylindrical beaker of base area `1500 cm^(2)`. When a mass m is kept on the wooden block the level of water rises in the beaker by 2mm. Find the mass m.

Text Solution

Verified by Experts

The correct Answer is:
`m = 300 gm`
Let the cube dips further by y cm and water level rises by 2 mm

Then equating the volume (`"/// volume =\\\"` volume in figure) `rArr` volume of water raised
= volume of extra depth of wood
`rArr 100y =(1500-100)(2)/(10)=1400`
`xx (2)/(10)=280`
`:. y =2.8 cm`
`:.` Extra upthrust
`rho_("water")xx(2.8 +0.2)xx 100g = mg rArr`
` m = 300 gm`
`m = 300 gm`
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