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Question
A metal cube of edge 5 cm and density 9 g cm-3 is suspended by a thread so as to be completely immersed in a liquid of density 1.2 g cm-3. Find the tension in thread. (Take g = 10 m s-2)
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Solution
Given, side of the cube = 5 cm
∴ volume of the cube = 5 × 5 × 5 = 125 cm3
Density of metal = 9.0 g cm-3
Density of liquid = 1.2 g cm-3
Mass of the cube = volume × density
= 125 × 9 = 1125 g
∴ weight of the cube = 1125 gf (downwards)
Upthrust on cube = weight of the liquid displaced
= volume of the cube × density of liquid × g
= 125 × 1.2 ×
= 150 gf (upwards)
Tension in thread = Net downward force
= Weight of cube - Upthrust on cube
= 1125 − 150
= 975 kgf
= 9.75 N ...[∵ g = 10 m s-2]
Hence, tension in thread = 9.75 N
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