A solid cube with a side length of 4 cm and density of 2 g/cm³ is submerged in a liquid. What is the buoyant force acting on the cube?2 marks32 N64 N16N8N

The buoyant force acting on an object submerged in a liquid is equal to the weight of the liquid displaced by the object. This is known as Archimedes' principle.

Here are the steps to calculate the buoyant force:

1. Calculate the volume of the cube: The volume (V) of a cube is given by the formula V = a³, where a is the length of a side. So, V = 4 cm * 4 cm * 4 cm = 64 cm³.

2. Calculate the weight of the liquid displaced: The weight (W) of the liquid displaced is equal to the volume of the cube times the density of the liquid. Assuming the density of the liquid is the same as the density of the cube (2 g/cm³), W = V * density = 64 cm³ * 2 g/cm³ = 128 g.

3. Convert the weight to Newtons: The weight in Newtons is given by the formula W = m * g, where m is the mass (in kg) and g is the acceleration due to gravity (approximately 9.8 m/s²). First, convert the mass from grams to kilograms (1 g = 0.001 kg), so m = 128 g * 0.001 kg/g = 0.128 kg. Then, W = 0.128 kg * 9.8 m/s² = 1.2544 N.

So, the buoyant force acting on the cube is approximately 1.2544 N. None of the options provided (32 N, 64 N, 16 N, 8 N) are correct.