The mass of a pendulum bob is m = 2kg and the length of the string is l. It is displaced through `90^(@)` from the vertical and released. What minimum tension (in N) should the string should be able to withstand so that it doesn't break during motion?

Answer

To solve the problem of finding the minimum tension that the pendulum string should withstand, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Parameters**:
- Mass of the pendulum bob, \( m = 2 \, \text{kg} \)
- Length of the string, \( l \) (not specified, but it will cancel out later)
- Angle of displacement from the vertical, \( \theta = 90^\circ \)

2. **Determine the Forces Acting on the Bob**:
- When the bob is at the lowest point of its swing, the forces acting on it are:
- The gravitational force acting downward, \( F_g = mg \)
- The tension in the string, \( T \), acting upward.

3. **Centripetal Force Requirement**:
- At the lowest point, the bob is moving in a circular path, so it requires a centripetal force, \( F_c \), given by:
\[ F_c = \frac{mv^2}{l} \]
- Here, \( v \) is the speed of the bob at the lowest point.

4. **Apply Newton's Second Law**:
- At the lowest point, the net force acting on the bob is the difference between the tension and the gravitational force:
\[ T - mg = F_c \]
- Rearranging gives:
\[ T = mg + \frac{mv^2}{l} \]

5. **Use Conservation of Energy**:
- The potential energy lost by the bob when it swings down from the height \( h \) (which is equal to the length of the string \( l \) when displaced by \( 90^\circ \)) is converted into kinetic energy:
\[ mgh = \frac{1}{2} mv^2 \]
- Since \( h = l \), we can write:
\[ mg l = \frac{1}{2} mv^2 \]
- Solving for \( v^2 \):
\[ v^2 = 2gl \]

6. **Substitute \( v^2 \) Back into the Tension Equation**:
- Substitute \( v^2 \) into the tension equation:
\[ T = mg + \frac{m(2gl)}{l} \]
- This simplifies to:
\[ T = mg + 2mg = 3mg \]

7. **Calculate the Tension**:
- Now substituting \( m = 2 \, \text{kg} \) and \( g = 10 \, \text{m/s}^2 \):
\[ T = 3 \times 2 \times 10 = 60 \, \text{N} \]

### Final Answer:
The minimum tension that the string should be able to withstand is **60 N**.