The ratio of velocity of two objects A and B is `1:3`. It the position-time graph of object A is inclined to time axis at `30^(@)`, then the position-time graph of object B is inclined to time axis at

A. `0^∘`
B. `90^∘`
C. `30^∘`
D. `60^∘`

Options

A. `0^(@)`
B. `90^(@)`
C. `30^(@)`
D. `60^(@)`

Answer

To solve the problem, we need to analyze the information given about the two objects A and B, particularly focusing on their velocities and the angles of their position-time graphs.

### Step-by-Step Solution:

1. **Understanding the Given Ratio of Velocities**:
The ratio of the velocities of objects A and B is given as \( v_A : v_B = 1 : 3 \). This means that if the velocity of object A is \( v_A \), then the velocity of object B is \( v_B = 3v_A \).

2. **Analyzing the Position-Time Graph of Object A**:
The position-time graph of object A is inclined to the time axis at an angle of \( 30^\circ \). The slope of a position-time graph gives us the velocity of the object. Therefore, we can express the velocity of object A in terms of the angle:
\[ v_A = \tan(30^\circ) \]

3. **Calculating \( \tan(30^\circ) \)**:
The value of \( \tan(30^\circ) \) is known:
\[ \tan(30^\circ) = \frac{1}{\sqrt{3}} \]
Thus, we have:
\[ v_A = \frac{1}{\sqrt{3}} \]

4. **Finding the Velocity of Object B**:
Since \( v_B = 3v_A \), we can substitute the value of \( v_A \):
\[ v_B = 3 \times \frac{1}{\sqrt{3}} = \frac{3}{\sqrt{3}} = \sqrt{3} \]

5. **Relating the Angles of the Position-Time Graphs**:
Let the angle of inclination of the position-time graph of object B be \( \theta \). The velocity of object B can also be expressed in terms of this angle:
\[ v_B = \tan(\theta) \]

6. **Setting Up the Equation**:
From the velocities we have:
\[ \tan(\theta) = \sqrt{3} \]

7. **Finding the Angle \( \theta \)**:
We know that:
\[ \tan(60^\circ) = \sqrt{3} \]
Therefore, we can conclude:
\[ \theta = 60^\circ \]

8. **Final Answer**:
The angle at which the position-time graph of object B is inclined to the time axis is \( 60^\circ \).

### Conclusion:
The correct answer is **D. \( 60^\circ \)**.