Question

The gate of a building is 3 m broad. It can be opened by applying 100 N force at the middle of the gate. Calculate the least force required to open this gate.( at a point 6m)

• A. 10 N
• B. 30 N
• C. 20 N
• D. 50 N

Answer 1

The correct option is D

50 N

Step 1: Given data and assumptions made

Initially the breadth of the gate, $L_1=3m$

Initially the force, $F_1=100N$

Finally the breadth of the gate, $L_2=6m$

Let the least force required to open this gate be F₂

Step 2: Explanation for the correct option

$$\begin{gathered} \mathrm{Moment}\mathrm{of}\mathrm{force}=\mathrm{Force}\times perpendicular\mathrm{distance} \\ \mathrm{Moment}\mathrm{of}\mathrm{force}=\mathrm{constant} \\ {\mathrm{F}}_1{\mathrm{L}}_1={\mathrm{F}}_2{\mathrm{L}}_2 \\ 100\mathrm{N}\times 3\mathrm{m}={\mathrm{F}}_2\times 6\mathrm{m} \\ {\mathrm{F}}_2=\frac{100N\times 3m}{6m} \\ {\mathrm{F}}_2=50\mathrm{N} \end{gathered}$$

Thus the least force required to open this gate is 50 N. Hence, D is the correct option.