Question

A door 1.6 m wide requires a force of 1 N to be applied at the free end to open or close it. The force that is required at a point 0.4 m distance from the hinges for opening or closing the door is

• A. 1.2 N
• B. 3.6 N
• C. 2.4 N
• D. 4 N

Hint:

The closer you are to the hinges, the more force you need to generate the same torque.

Answer 1

The Correct Option is D

Step 1: Torque Concept
Torque ($\tau$) required to move the door remains constant: $\tau = F \times d$.
Step 2: Initial Torque
$\tau = 1 \text{ N} \times 1.6 \text{ m} = 1.6 \text{ N-m}$.
Step 3: New Force
For $d = 0.4 \text{ m}$, $F = \frac{\tau}{d} = \frac{1.6}{0.4} = 4$ N.
Final Answer: (d)