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 determining the minimum tension that the string of a pendulum should withstand when the bob is displaced through \(90^\circ\) from the vertical and released, we can follow these steps:

### Step 1: Understand the Initial Conditions
The pendulum bob has a mass \( m = 2 \, \text{kg} \) and is displaced to an angle of \( 90^\circ \) from the vertical. At this position, the bob is at its maximum height.

### Step 2: Calculate the Height
When the pendulum is at \( 90^\circ \), the height \( h \) above the lowest point can be calculated using the length of the string \( l \):
\[ h = l \]

### Step 3: Use Conservation of Energy
At the highest point, all the energy is potential energy (PE), which can be expressed as:
\[ PE = mgh = mg \cdot l \]
When the pendulum bob swings down to the lowest point, this potential energy converts into kinetic energy (KE):
\[ KE = \frac{1}{2} mv^2 \]
By conservation of energy:
\[ mgl = \frac{1}{2} mv^2 \]
Cancelling \( m \) from both sides (since \( m \neq 0 \)):
\[ gl = \frac{1}{2} v^2 \]

### Step 4: Solve for Velocity
Rearranging the equation gives:
\[ v^2 = 2gl \]

### Step 5: Analyze Forces at the Lowest Point
At the lowest point of the swing, the forces acting on the bob are:
1. The tension \( T \) in the string acting upwards.
2. The weight \( mg \) acting downwards.

Using Newton's second law, the net force acting on the bob at the lowest point is:
\[ T - mg = \frac{mv^2}{l} \]
Substituting \( v^2 \) from the previous step:
\[ T - mg = \frac{m(2gl)}{l} \]
This simplifies to:
\[ T - mg = 2mg \]

### Step 6: Solve for Tension
Rearranging gives:
\[ T = 2mg + mg = 3mg \]
Substituting \( m = 2 \, \text{kg} \) and \( g = 10 \, \text{m/s}^2 \):
\[ T = 3 \cdot 2 \cdot 10 = 60 \, \text{N} \]

### Conclusion
The minimum tension that the string should be able to withstand is:
\[ \boxed{60 \, \text{N}} \]