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Question
An aluminium cube of side 5 cm and RD. 2.7 is suspended by a thread in alcohol of relative density 0.80. Find the tension in thread.
Solution
Side of an aluminium cube = l = 5 cm
Volume of aluminium cube = V = Z3 = (5)3 =125 cm3
Relative density of aluminium = R.D. = 2.7
Relative density of alcohol = R.D. = 0.80
Density of water = 1 g cm-3
R.D. of aluminium = `"Density of aluminium"/"Density of water"`
`2.7 = "Density of aluminium"/1`
Density of aluminium =ρ = 2.7 g cm-3
Mass of aluminium = V x ρ
m = 125 x 2.7 = 337.5 g
Wt. of aluminium cube acting downwards = 337.5 gf
Volume of alcohol displaced = Volume of cube = V = 125 cm3
Upthrust due to alcohol = `"V"xxrho_"alcohol" xx "g"`
Now R.D. of alcohol = `rho_"alcohol"/"Density of water"`
`0.80 = rho_"alcohol"/1`
`rho_"alcohol" = 0.80` g cm-3
⇒ Upthrust due to alcohol = `"V" xx rho_"alcohol" xx "g"`
= 125 × 0.80 × g = 100 gf
So tension in threat = Wt. of aluminium cube - Upthrust
= 337.5 - 100 = 237.5 gf
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