A cubic wooden block of side $2 ext{ m}$ is lying on a tabletop. If the mass of the wooden block is $10 ext{

Question

A cubic wooden block of side $2	ext{ m}$ is lying on a tabletop. If the mass of the wooden block is $10	ext{ kg}$, then the pressure exerted by the wooden block on the tabletop is: (consider $g = 10	ext{ m/s}^2$)

Examoogle · Accepted Answer

The correct answer is Option A: $25	ext{ N m}^{-2}$. Pressure is defined as the force acting normally per unit surface area. For a cubic wooden block resting on a tabletop, the force acting downwards is its weight ($W = mg$), and the area of contact is the area of one face of the cube ($A = 	ext{side}^2$). Using the given values, the pressure is calculated as $$P = \frac{mg}{	ext{side}^2} = \frac{10 	imes 10}{2 	imes 2} = \frac{100}{4} = 25 	ext{ N m}^{-2}$$.

Step-by-Step Solution & Concepts:
Pressure is defined as the force acting normally per unit surface area. For a cubic wooden block resting on a tabletop, the force acting downwards is its weight ($W = mg$), and the area of contact is the area of one face of the cube ($A = 	ext{side}^2$). Using the given values, the pressure is calculated as $$P = \frac{mg}{	ext{side}^2} = \frac{10 	imes 10}{2 	imes 2} = \frac{100}{4} = 25 	ext{ N m}^{-2}$$.

Working Principle: When a solid body rests on a surface, it exerts a perpendicular force due to gravity, which is equal to its weight ($W = mg$). The pressure ($P$) distributed across the contact area ($A$) is given by $P = \frac{F}{A}$. Since the block is a cube with a side length of $2	ext{ m}$, the area of its base in contact with the tabletop is $2	ext{ m} 	imes 2	ext{ m} = 4	ext{ m}^2$. Substituting $m = 10	ext{ kg}$ and $g = 10	ext{ m/s}^2$, the total force (weight) is $100	ext{ N}$. Dividing $100	ext{ N}$ by $4	ext{ m}^2$ yields a pressure of $25	ext{ N/m}^2$ or $25	ext{ Pa}$.

Key Formulas: $P = \frac{F}{A}$ — Pressure formula where F is force and A is area; $W = mg$ — Weight formula representing force due to gravity; $A = 	ext{side}^2$ — Area of one face of a cube

Key Points: Pressure is inversely proportional to the surface area for a constant applied force.; The SI unit of pressure is Pascal (Pa) or $	ext{N m}^{-2}$.; Here, mass $m = 10	ext{ kg}$ and acceleration due to gravity $g = 10	ext{ m/s}^2$, giving a total force of $100	ext{ N}$.; The contact area is the area of one face of the cube: $2	ext{ m} 	imes 2	ext{ m} = 4	ext{ m}^2$.

Advantages: Helps understand force distribution across different surface areas in structural engineering.

Applications: Designing foundations for buildings and bridges to prevent excessive ground pressure.; Understanding why sharp knives cut better due to a smaller surface area concentrating pressure.

Additional Info: Option A ($25	ext{ N m}^{-2}$) is correctly derived by dividing $100	ext{ N}$ by $4	ext{ m}^2$.. Incorrect options like $30$, $20$, and $15	ext{ N m}^{-2}$ result from arithmetic errors in calculating the area or weight.

Answer: A is correct — The pressure exerted by the wooden block on the tabletop is 25 N m⁻².

Exam Tip: Always check whether the entire weight or only a component of it acts perpendicularly to the surface when calculating pressure on inclined planes.

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