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 body of volume V and density ρ is kept completely immersed in a liquid of density ρL. If g is the acceleration due to gravity, then write expressions for the following:
(i) The weight of the body, (ii) The upthrust on the body,
(iii) The apparent weight of the body in liquid, (iv) The loss in weight of the body.
How does the density of material of a body determine whether it will float or sink in water?
The density of iron is 7.8 x 103 kg m-3. What is its relative density?
A solid weighs 120 gf in air and and 105 gf when it is completely immersed in water. Calculate the relative density of solid.
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 volume 100 cm3 weighs 1 kgf in air. Find:
- Its weight in water and
- Its relative density.
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.
