Advertisements
Advertisements
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.
Advertisements
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
APPEARS IN
RELATED QUESTIONS
A sphere of iron and another sphere of wood of the same radius are held under water. Compare the upthrust on the two spheres.
[Hint: Both have equal volume inside the water].
The relative density of silver is 10.8. Find its density.
A solid weighs 32 gf in air and 28.8 gf in water. Find: (i) The volume of solid, (ii) R.D. of solid and (iii) The weight of solid in a liquid of density 0.9 g cm-3.
A piece of stone of mass 113 g sinks to the bottom in water contained in a measuring cylinder and water level in cylinder rises from 30 ml to 40 ml. Calculate R.D. of stone.
A body of mass 70 kg, when completely immersed in water, displaces 20,000 cm3 of water. Find: (i) The weight of body in water and (ii) The relative density of material of the body.
A solid of density 7600 kgm3 is found to weigh 0.950 kgf in air. If 4/5 volume of solid is completely immersed in a solution of density 900 kgm3, find the apparent weight of solid in a liquid.
A cube of the lead of side 8 cm and R.D. 10.6 is suspended from the hook of a spring balance. Find the reading of spring balance. The cube is now completely immersed in sugar solution of R.D. 1.4. Calculate the new reading of spring balance.
A cylinder made of copper and aluminium floats in mercury of density 13.6 gem-3, such that 0.26th part of it is below mercury. Find the density of solid.
Calculate the mass of a body whose volume is 2m3 and relative density is 0.52.
A body of volume 100 cm3 weighs 1 kgf in air. Calculate its weight in water. What is its relative density?
