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Two metallic spheres 'P' and 'Q' weighin...

Two metallic spheres 'P' and 'Q' weighing 200 gwt and 150 gwt, respectively, balance each other when immersed in water. If the relative density of 'P' is 2 find the specific gravity of 'Q'.

Text Solution

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Weight of P in air, `W_(1p)=200 gwt`
Let weight of P in water be `W_(2p)`
`therefore` the apparent loss of weight of 'P' in water `=W_(1p)-W_(2p)`
`therefore` the relative density of 'P' `(W_(1p))/(W_(1p)-W_(2p))=2` (given)
`therefore (200)/(200-W_(2p))=2 implies W_(2p)`
`=200(1-(1)/(2))=100g _(wt)`
Weight of 'Q' in ari, `W_(1q)=150` gwt
Let weight of 'Q' in water be `W_(2p)`
`therefore` the apparent loss of weight of 'Q' in water
`=W_(1p)-W_(2p)=150-W_(2q)`
But `W_(2p)=W_(2q)`
`therefore` apparent loss of weight of 'Q' in water
=150-100=50 gwt
`therefore` the specific gravity of `Q=(W_(1q))/(W_(1q)-W_(2q))=(150)/(50)=3`
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