A pendulum bob of mass 50 gm is suspended from the ceiling of an elevator. The tension in the string if the elevator goes up with uniform velocity is approximately

Options

A. 0.30 N
B. 0.40 N
C. 0.42 N
D. 0.50 N

Answer

To solve the problem of finding the tension in the string of a pendulum bob suspended in an elevator moving upwards with uniform velocity, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Mass of the pendulum bob, \( m = 50 \, \text{grams} = 0.05 \, \text{kg} \) (since \( 1 \, \text{kg} = 1000 \, \text{grams} \)).
- Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \).
- The elevator is moving upwards with uniform velocity, which means the acceleration \( a = 0 \).

2. **Understand the Forces Acting on the Pendulum Bob:**
- The two forces acting on the pendulum bob are:
- The tension \( T \) in the string acting upwards.
- The weight of the bob acting downwards, given by \( W = mg \).

3. **Set Up the Equation of Motion:**
- According to Newton's second law, the net force acting on the pendulum bob can be expressed as:
\[ T - mg = ma \]
- Since the elevator is moving with uniform velocity, the acceleration \( a = 0 \). Therefore, the equation simplifies to:
\[ T - mg = 0 \]

4. **Solve for Tension \( T \):**
- Rearranging the equation gives:
\[ T = mg \]
- Substitute the values of \( m \) and \( g \):
\[ T = 0.05 \, \text{kg} \times 10 \, \text{m/s}^2 \]
\[ T = 0.5 \, \text{N} \]

5. **Conclusion:**
- The tension in the string when the elevator goes up with uniform velocity is approximately \( 0.5 \, \text{N} \).

### Final Answer:
The tension in the string is approximately **0.5 N**.

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