A stone is dropped from a height of 80 m (take g = 10 m/s²). Find: (a) time to reach the ground, (b) velocity on impact. Then: A wooden block of mass 500 g and volume 800 cm³ is placed in water (density 1 g/cm³). Find the upthrust. Does the block float or sink?

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Accepted Answer

STONE DROP: u = 0 (dropped from rest), a = g = 10 m/s² (downward), s = 80 m. (a) Using s = ut + ½at²: 80 = 0×t + ½×10×t². 80 = 5t². t² = 16. t = 4 seconds. (b) Using v = u + at: v = 0 + 10×4 = 40 m/s. [Check: v² = u² + 2as = 0 + 2×10×80 = 1600. v = 40 m/s ✓]. ARCHIMEDES / FLOATATION: Mass of block = 500 g = 0.5 kg. Volume of block = 800 cm³ = 800 × 10⁻⁶ m³ = 8 × 10⁻⁴ m³. UPTHRUST = Weight of water displaced = Volume × density of water × g = 800 cm³ × 1 g/cm³ × g = 800 g = 0.8 kg weight (if fully submerged). Weight of block = 500 g. Since weight of block (500 g) < weight of water displaced if fully submerged (800 g), the block FLOATS. It will submerge only until upthrust = weight of block. Volume submerged = mass/density of water = 500 g / 1 g/cm³ = 500 cm³. So 500 cm³ is submerged (62.5% of the block), 300 cm³ is above water. UPTHRUST (actual) = 500 g-force (= weight of block). The block FLOATS with 500/800 = 62.5% of its volume submerged.

Practice — Physics — Motion, Laws of Motion, Fluids, Heat, Light & Electricity

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