The tension in the rope is equal to the centripetal force on the rocket.

Definition of velocity:

The time necessary to go around one circle is it's period, which is the inverse of the frequency.

Doubling the frequency would double the velocity, which would quadruple the tension.

The bus going around a corner is experiencing centripetal acceleration towards the center of it's turn. Even though the linear velocity is constant (speed), the bus is constantly changing directions, thus its velocity is not constant. Since acceleration is defined as the change in velocity over time, the acceleration is nonzero, which means that due to Newton's second law, the net force on the bus is also nonzero.

To calculate the centripetal acceleration at the point identified in the expression (which is simply ), we need to determine the linear velocity at this point. We can do this by using the period of the bowling ball:

Where both the circumference and velocity are referenced to the outer surface of the bowling ball:

Plugging in our values, we get:

This is the time it takes for any single point of the ball (inside or out, excluding the center) to complete one full rotation. Therefore, we can apply this same expression to the point asked in the question (r=0.05m):

Rearranging for velocity, we get:

Plugging in our values, we get:

The total kinetic energy of a solid sphere can be calculated using the following:

Where I is the moment of inertia for a solid sphere:

And w is the angular velocity:

Plugging these in, we get:

We can obtain an expression for velocity using the expression for centripetal acceleration:

Rearranging:

Plugging this in, we get:

We have all of these values, so let's plug them in:

At the top of the swing, both gravity and the tension of the string will be in the same direction, thus, this is where tension would be at a minimum. 

At the very limit of being taught, 

Thus,

Solving for 

This will be the linear velocity.

The angular velocity will be 

Combining equations

Plugging in values

At the top of the swing, both gravity and the tension of the string will be in the same direction, thus, this is where tension would be at a minimum. 

At the very limit of being taught, 

Thus,

Solving for 

This will be the linear velocity.

The angular velocity will be 

Combining equations

Plugging in values

Let's go through each answer choice one by one. The force of gravity on the ball is always its mass times gravity, which is constant. The string's pull on the ball is always perpendicular to the ball's motion, so it isn't doing any work, and thus has a constant rate of work . The ball's angular momentum is always constant since its mass, the radius of the circle it's traveling in, and its speed are constant. The only the changing is the tension in the string. This is true because the ball needs the same center pulling force (centripetal force) throughout its path, but this centripetal force is constantly changing direction. For example, at the top of its path, the centripetal force must be down because that's the direction of the center of its circle of motion, but at the bottom, the centripetal force must be up. There are two forces on the ball, gravity and tension. The force of gravity is always down and constant, so the tension needs to change in order to keep the center pulling force the same. For example, when the ball is at the bottom of the circle, the force of gravity is away from the center of the circle, so tension must be higher to keep the center pull constant.

Circumference of a circle:

Distance plane travels during loop (which will be the circumference)

Centripetal acceleration:

Plugging in values:

Circumference of a circle:

Distance plane travels during loop (which will be the circumference)

Centripetal acceleration:

Plugging in values:

Circumference of a circle:

Distance plane travels during loop (which will be the circumference)