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Standard IX

Mathematics

Volume of a cuboid

A metal cube ...

Question

A metal cube of edge $5 c m$ and density $9 g c m^{- 3}$ is suspended by a thread so as to be completely immersed in a liquid of density $1.2 g c m^{- 3}$ . The tension in thread is X N. Find X.

11.25

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12.00

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9.25

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9.75

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Solution

The correct option is A $9.75$
Side of the cube $= 5 c m$
So, its volume , $V = a^{3} = 125 c m^{3}$
Mass of cube $= V \times d = 125 \times 9 = 1125 g$
Weight $= m g = 1125 \times 1000 = 1125000 d y n e$
Now, cube is immersed is liquid,
$∴$ buoynat force $= V ρ g = 125 \times 1.2 \times 1000 = 150000 d y n e$
So, Tension = apparent weight $= (1125000 - 150000) d y n e = 975000 d y n e = 9.75 N$

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A metal cube of edge 5 cm and density 9 gcm−3 is suspended by a thread so as to be completely immersed in a liquid of density 1.2 gcm−3. The tension in thread is X N. Find X.

A metal cube of edge $5 c m$ and density $9 g c m^{- 3}$ is suspended by a thread so as to be completely immersed in a liquid of density $1.2 g c m^{- 3}$ . The tension in thread is X N. Find X.