A rectangular solid block has length 10cm, breadth 5cm and height 2cm. If it lies on a horizontal surface, and…

1. Analyze the question

We are given the dimensions of a rectangular block (length, breadth, and height) and its density. We need to calculate the pressure it exerts on a horizontal surface.

Given:

• Length ($l$) = 10 cm = 0.1 m
• Breadth ($b$) = 5 cm = 0.05 m
• Height ($h$) = 2 cm = 0.02 m
• Density ($\rho$) = 100 kg/m³
• Acceleration due to gravity ($g$) = 10 m/s² (standard value used in JAMB)

2. Explain the concept

• Pressure ($P$): Defined as Force per unit area ($P = \frac{F}{A}$).
• Force ($F$): In this case, the force is the weight of the block ($F = mg$).
• Mass ($m$): Calculated as Density $\times$ Volume ($m = \rho \times V$).
• Volume ($V$): $l \times b \times h$.
• Area ($A$): The surface area in contact with the ground is $l \times b$.

Shortcut Formula: For a solid block of uniform density, the pressure exerted on the surface it rests on can be simplified: $P = \frac{mg}{A} = \frac{(\rho \times V) \times g}{A} = \frac{\rho \times (l \times b \times h) \times g}{l \times b}$ The $(l \times b)$ cancels out, leaving: $P = \rho \times h \times g$

3. Show the solution

Using the simplified formula: $P = \rho \times h \times g$

• $\rho = 100 \text{ kg/m}^3$
• $h = 0.02 \text{ m}$
• $g = 10 \text{ m/s}^2$

$P = 100 \times 0.02 \times 10$ $P = 100 \times 0.2$ $P = 20 \text{ N/m}^2$

4. Identify the answer

The calculated pressure is 20 N/m². This matches Option A.

5. Tip

When calculating pressure for a solid block, you don't always need to calculate the total mass and total area separately. If the block is uniform, the pressure is simply the product of its density, its height, and gravity ($P = \rho gh$). This is the same formula used for liquid pressure! Always ensure your units are in SI (meters, kilograms, seconds) before calculating.