A body rotates about a fixed axis with an angular acceleration of `3 rad//s^(2)` The angle rotated by it during the time when its angular velocity increases frm 10 rad/s to 20 rad/s (in radian) is

Options

A. 50
B. 100
C. 150
D. 200

Explanation

To solve the problem, we can use the kinematic equation for rotational motion. The equation that relates angular displacement (θ), initial angular velocity (ω₁), final angular velocity (ω₂), and angular acceleration (α) is:

\[ \theta = \frac{\omega_2^2 - \omega_1^2}{2\alpha} \]

Where:
- θ is the angular displacement in radians,
- ω₁ is the initial angular velocity,
- ω₂ is the final angular velocity,
- α is the angular acceleration.

### Step 1: Identify the given values
From the problem, we have:
- Angular acceleration, α = 3 rad/s²
- Initial angular velocity, ω₁ = 10 rad/s
- Final angular velocity, ω₂ = 20 rad/s

### Step 2: Substitute the values into the equation
Now, we can substitute the known values into the equation:

\[ \theta = \frac{(20 \, \text{rad/s})^2 - (10 \, \text{rad/s})^2}{2 \cdot 3 \, \text{rad/s}^2} \]

### Step 3: Calculate the squares of the angular velocities
Calculating the squares:

\[ (20 \, \text{rad/s})^2 = 400 \, \text{rad}^2/\text{s}^2 \]
\[ (10 \, \text{rad/s})^2 = 100 \, \text{rad}^2/\text{s}^2 \]

### Step 4: Substitute the squared values into the equation
Now, substituting these values back into the equation:

\[ \theta = \frac{400 \, \text{rad}^2/\text{s}^2 - 100 \, \text{rad}^2/\text{s}^2}{2 \cdot 3 \, \text{rad/s}^2} \]

### Step 5: Simplify the equation
This simplifies to:

\[ \theta = \frac{300 \, \text{rad}^2/\text{s}^2}{6 \, \text{rad/s}^2} \]

### Step 6: Calculate the angular displacement
Now, performing the division:

\[ \theta = 50 \, \text{radians} \]

### Final Answer
The angle rotated by the body during the time when its angular velocity increases from 10 rad/s to 20 rad/s is **50 radians**.

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