Introduction:
In this question, we are given a pendulum at rest which is given a sharp hit to impart a horizontal velocity. We need to find the tension in the string when the pendulum makes an angle of 60 degrees with the vertical. To solve this problem, we will use the principles of conservation of energy and forces acting on the pendulum.

Given:
- Initial velocity imparted to the bob = √(10mgl)
- Angle made by the bob with the vertical = 60 degrees

Analysis:
When the pendulum is at rest, the tension in the string is equal to the weight of the bob, which is mg. However, when the bob is given a horizontal velocity, it will start moving in a circular path due to the tension in the string.

Conservation of Energy:
At the highest point of the pendulum's swing, the tension in the string is equal to zero, and the entire energy is in the form of gravitational potential energy. At this point, the velocity of the bob is zero.

Forces Acting on the Pendulum:
When the pendulum makes an angle θ with the vertical, the forces acting on the bob can be resolved into two components:
- The component of weight in the direction of motion (mgcosθ), which provides the centripetal force for circular motion.
- The component of weight perpendicular to the direction of motion (mgsinθ), which provides the restoring force for the pendulum.

Calculations:
1. Let's assume the length of the pendulum is 'l'.
2. At the highest point of the swing, the velocity of the bob is zero, so the tension in the string is equal to the weight of the bob, which is mg.
3. Using the conservation of energy, we can equate the initial kinetic energy of the bob to its final gravitational potential energy at the highest point of the swing.
1/2 * mv² = mgh
1/2 * m * (√(10mgl))² = mgl(1 - cosθ)
5gl = l(1 - cosθ)
5g = 1 - cosθ
cosθ = 1 - 5g

Conclusion:
The tension in the string when the pendulum makes an angle of 60 degrees with the vertical is equal to the weight of the bob, which is mg, where g is the acceleration due to gravity.