A cubical block of side 1 m and mass 1 kg is pulled by a force F applied to central line so that it slides with an acceleration of `1m//s^(2)` . What is the net torque on it about O. (in N-m).

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Identify the Given Data
- Side of the cubical block (s) = 1 m
- Mass of the block (m) = 1 kg
- Acceleration of the block (a) = 1 m/s²

### Step 2: Calculate the Force Acting on the Block
Using Newton's second law of motion, the force (F) can be calculated as:
\[ F = m \cdot a \]
Substituting the known values:
\[ F = 1 \, \text{kg} \cdot 1 \, \text{m/s}^2 = 1 \, \text{N} \]

### Step 3: Determine the Perpendicular Distance from Point O
Since the force is applied at the central line of the block, the perpendicular distance (d) from point O to the line of action of the force is half the side length of the cube:
\[ d = \frac{s}{2} = \frac{1 \, \text{m}}{2} = 0.5 \, \text{m} \]

### Step 4: Calculate the Torque about Point O
Torque (τ) is calculated using the formula:
\[ \tau = F \cdot d \]
Substituting the values we have:
\[ \tau = 1 \, \text{N} \cdot 0.5 \, \text{m} = 0.5 \, \text{N} \cdot \text{m} \]

### Final Answer
The net torque on the cubical block about point O is:
\[ \tau = 0.5 \, \text{N} \cdot \text{m} \]

---