A travelling crane as shown is used to carry a load of two tonnes at point D. A counter mass CW is to be added as shown to avoid toppling of the crane. Find the limiting value of counter mass and distance, X from F, such that it will not topple the crane even in the absence of load at D. The mass of the crane may be taken as 2 tonnes and is acting 2 meters away from E towards D.

Correct option is A

​$$\textbf{Moments About Fulcrum } F: \\\text{1. Crane's Moment (Clockwise):} \\M_{\text{crane}} = W \times (\text{EF} + \text{distance from } E) = 19{,}620 \, \text{N} \times (6\, \text{m} + 2\, \text{m}) = 156{,}960 \, \text{Nm}\\[1em]\text{2. Counter Mass Moment (Counter-Clockwise):} \\M_{\text{CW}} = CW \times X\\[1em]\textbf{Equilibrium Condition:} \\\text{To prevent toppling:} \\M_{\text{CW}} \geq M_{\text{crane}} \Rightarrow CW \times X \geq 156{,}960 \, \text{Nm}\\[2em]\textbf{Step 2: Solve for } CW \text{ and } X \\\text{Given: } CW = 2 \, \text{tonnes} = 19{,}620 \, \text{N}, \quad X = 8 \, \text{m} \\CW \times X = 19{,}620 \, \text{N} \times 8 \, \text{m} = 156{,}960 \, \text{Nm}$$​​