A rectangular block 2 m long, 1 m wide and 1 m deep floats in water, the depth of immersion being 0.5 m. If water weighs 10 kN/m³, then the weight of the block is

Solution (By Examveda Team)

Understanding the Problem:
Imagine a wooden block floating in a swimming pool. The block is partially submerged; only a portion of it is underwater.
The question asks us to find the weight of this block.

Key Concept: Buoyancy
When an object floats, the upward force of the water (called buoyant force) equals the weight of the object.
The buoyant force is equal to the weight of the water displaced by the submerged part of the object.

Calculations:
1. Find the volume of water displaced:
The block is submerged to a depth of 0.5 m. The area of the submerged part is length x width = 2 m x 1 m = 2 m².
The volume of water displaced is area x depth = 2 m² x 0.5 m = 1 m³

2. Calculate the weight of the displaced water:
Water weighs 10 kN/m³. Therefore, the weight of 1 m³ of water is 1 m³ x 10 kN/m³ = 10 kN

3. Determine the weight of the block:
Since the block is floating, the weight of the block equals the buoyant force (weight of the displaced water).
Therefore, the weight of the block is 10 kN

Correct Answer:
The correct option is B: 10 kN