| (i) Upthrust | = | loss in weight |
| = | 55−49 | |
| = | 6 gf | |
| (ii) Weight of water displaced | = | upthrust |
| = | 6 gf | |
| Since the density of water is 1 g cm−3, | ||
| ∴ volume of water displaced | = | 6 cm3 |
| But the solid displaces water equal to its own volume, | ||
| ∴ volume of solid | = | 6 cm3 |
| (iii) R.D. of solid | = | (Weight of solids in air) / (Weight in air – Weight in water) |
| = | (55) / (55 – 49) | |
| = | 55/6 | |
| = | 8.33 |
A metal cube of side 7 cm and density 7.9 g cm–3 is suspended by a thread and is immersed completely in a liquid of density 1.1 g cm–3. Find the tension in the thread?
| Volume of the cube | = | 7 × 7 × 7 = 343 cm3 |
| Mass of the cube | = | Volume × density |
| = | 343 cm3 × 7.9 g cm–3 | |
| = | 2709.7 g. | |
| ∴ Weight of the cube | = | 2709.7 gf (downwards) |
| Upthrust on cube | = | Weight of liquid displaced |
| = | Volume of cube × density of liquid | |
| = | 343 × 1.1 gf = 377.3 gf (upwards) | |
| ∴ Tension in the thread | = | Net downward force |
| = | Weight of cube − Upthrust on cube | |
| = | 2709.7 − 377.3 | |
| = | 2332.4 gf |
| Weight in air | = | 240 gf |
| Weight in water | = | 230 gf |
| (i) Loss in weight of the body | = | 240 gf − 230 gf |
| = | 10 gf | |
| (ii) Upthrust on the body | = | loss in weight |
| = | 10 gf |