Three children are sitting on a see-saw in such a way that is balances. A `20 kg` and a `30 kg` boy are on opposite sides at a distance of `2m` from the pivot. It the third boy jumps off, thereby destroying balance, then the initial angular acceleration of the board is: (Neglect weight of board)

Options

A. A. `0.01rads^(-2)`
B. B. `1.0rads^(-2)`
C. C. `10 rads^(-2)`
D. D. `100rads^(-2)`

Explanation

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

### Step 1: Understand the Initial Conditions
We have two boys on a seesaw, one weighing 20 kg (m1) and the other weighing 30 kg (m2). They are positioned 2 meters away from the pivot on opposite sides, and the seesaw is balanced initially.

### Step 2: Identify the Forces and Torques
When the third boy jumps off, the seesaw will no longer be balanced. The forces acting on the seesaw due to the weights of the two boys will create torques about the pivot.

- The torque due to m1 (20 kg) is given by:
\[ \tau_1 = m_1 \cdot g \cdot r_1 = 20 \cdot g \cdot 2 \]

- The torque due to m2 (30 kg) is given by:
\[ \tau_2 = m_2 \cdot g \cdot r_2 = 30 \cdot g \cdot 2 \]

### Step 3: Calculate the Net Torque
The net torque (τ_net) acting on the seesaw is the difference between the torques due to m2 and m1:
\[ \tau_{net} = \tau_2 - \tau_1 = (30 \cdot g \cdot 2) - (20 \cdot g \cdot 2) \]

Substituting \(g = 10 \, \text{m/s}^2\):
\[ \tau_{net} = (30 \cdot 10 \cdot 2) - (20 \cdot 10 \cdot 2) = 600 - 400 = 200 \, \text{N m} \]

### Step 4: Calculate the Moment of Inertia
The moment of inertia (I) of the system can be calculated using the formula:
\[ I = m_1 \cdot r_1^2 + m_2 \cdot r_2^2 \]
Substituting the values:
\[ I = (20 \cdot 2^2) + (30 \cdot 2^2) = (20 \cdot 4) + (30 \cdot 4) = 80 + 120 = 200 \, \text{kg m}^2 \]

### Step 5: Calculate Angular Acceleration
Using the relationship between torque and angular acceleration:
\[ \tau_{net} = I \cdot \alpha \]
We can rearrange this to find the angular acceleration (α):
\[ \alpha = \frac{\tau_{net}}{I} = \frac{200}{200} = 1 \, \text{rad/s}^2 \]

### Final Answer
The initial angular acceleration of the seesaw after the third boy jumps off is:
\[ \alpha = 1 \, \text{rad/s}^2 \]

---