A

Step 1: Understand the system. The pendulum of mass m is released from a horizontal position.
Step 2: At the lowest point (equilibrium position), the forces acting on the pendulum are:

• Gravitational force ( = mg, acting downward).
• Tension in the string (T, acting upward).

Step 3: At this position, the net force must provide the required centripetal force to keep the pendulum moving in a circular path.
The centripetal force is given by \( F_c = \frac{mv^2}{\ell} \), where v is the speed of the pendulum at the lowest point, and \( \ell \) is the length of the string.
Step 4: At the lowest point, we can write the equation:
\( T - mg = \frac{mv^2}{\ell} \)
Therefore, the tension T is given by:
\( T = mg + \frac{mv^2}{\ell} \)
Step 5: To find the speed v at the lowest point, we can use conservation of energy. The potential energy at the top is converted to kinetic energy at the bottom:
\( mgh = \frac{1}{2} mv^2 \).
The height h is equal to the length of the string \(  \) (since it drops from horizontal to vertical position), so:
\( mgl = \frac{1}{2} mv^2 \) which gives \( v^2 = 2gl \).
Step 6: Substitute v² back into the tension equation:
\( T = mg + \frac{m(2gl)}{\ell} = mg + 2mg = 3mg \).
Step 7: Thus, the minimum strength of the string must be able to withstand the maximum tension, which is \( T_{min} = 3mg \).
Therefore, the answer is option A: 3mg.