An increase/decrease in which of the following variables would have the greatest effect on the period of a simple pendulum?

We have no idea what those "following variables" are.  You faded out right at the point where you were supposed to show them to us.

The period of a simple pendulum only depends on its length, and the acceleration of gravity in the place where the pendulum is swinging.

It's really tough to answer the question, because both of these things are in a fraction in the formula for the period . . . the length is the numerator, and the local acceleration of gravity is the denominator.  So which one has a greater effect on the period really depends on what those numbers are before anything changes.  

we need to know the time interval during which the force acts. impulse of force = momentum change

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2