Question

The resultant soil thrust and radial force acting on each gang of a single acting disc harrow are 1200 N, and 600 N respectively. The resultant downward force acting on each gang is 2400 N. The perpendicular distance of the soil thrust from the gang axis is 20 cm. What is the distance between line of action of downward force and centre of the gang to get a uniform depth of cut?

• A. 5 cm
• B. 10 cm
• C. 15 cm
• D. 40 cm

Hint:

Note the simple ratio of forces:
The downward force (2400 N) is exactly twice the soil thrust (1200 N).
Therefore, its moment arm \(x\) must be exactly half of the thrust height (20 cm), which gives \(x = 10\text{ cm}\).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
To achieve a uniform depth of cut along a disc harrow gang, the clockwise turning moment caused by horizontal soil forces must be perfectly balanced by the counter-clockwise moment of the offset downward vertical force.

Step 2: Key Formula or Approach:
Taking moments about the center of the gang:
\[ \text{Turning Moment of Soil Thrust} = \text{Moment of Downward Force} \] \[ H \times h = W \times x \]

Step 3: Detailed Explanation:
Given values:
- Horizontal soil thrust (\(H\)) = \(1200\text{ N}\)
- Height of thrust from gang axis (\(h\)) = \(20\text{ cm}\)
- Resultant downward weight/force (\(W\)) = \(2400\text{ N}\)
Let the horizontal distance from the downward force to the gang center be \(x\).
Equating the moments:
\[ 1200 \text{ N} \times 20 \text{ cm} = 2400 \text{ N} \times x \] \[ 24000 = 2400 \times x \] \[ x = \frac{24000}{2400} = 10 \text{ cm} \]

Step 4: Final Answer:
The correct option is 2, which corresponds to 10 cm.