Calculate the upthrust on an object of volume 50cm3 which is immersed in liquid of density $10^{3}$ kgm-3 [g = 10$ms^{-2}$]

Analyze the question: We need the upthrust (buoyant force) on an object fully immersed in a liquid. The volume, liquid density and g are given.

Concept: By Archimedes' principle, the upthrust equals the weight of the liquid displaced:

Upthrust = V × ρ × g

where V is the volume of liquid displaced (equal to the volume of the object, since it is fully immersed), ρ is the density of the liquid, and g is the acceleration due to gravity.

Solution:

1. Convert the volume to m³: 50 cm³ = 50 × 10⁻⁶ m³ = 5 × 10⁻⁵ m³

2. Substitute the values: Upthrust = (5 × 10⁻⁵) × (10³) × 10 = 5 × 10⁻⁵ × 10⁴ = 5 × 10⁻¹ = 0.5 N

Answer: The upthrust is 0.5 N, which is option C.

Tip: The most common mistake is forgetting to convert cm³ to m³. Remember 1 cm³ = 10⁻⁶ m³. Also, with ρ = 1000 kg/m³ (water-like) and g = 10, every 100 cm³ gives 1 N of upthrust, so 50 cm³ gives 0.5 N. You can use this as a quick check in the exam.