A ball is attached to a string of length 3 m to make a pendulum. The pendulum is placed at a location that is away from the Earth's surface by three times the radius of the Earth. What is the acceleration due to gravity (in m/s2) at that height and what is the period (in s) of the oscillations

1)

2) 13.9 s

Explanation:

1)

The acceleration due to gravity is the acceleration that an object in free fall (acted upon the force of gravity only) would have.

It can be calculated using the equation:

(1)

where

G is the gravitational constant

is the Earth's mass

r is the distance of the object from the Earth's center

The pendulum in the problem is at an altitude of 3 times the radius of the Earth (R), so its distance from the Earth's center is

where

is the Earth's radius

Therefore, we can calculate the acceleration due to gravity at that height using eq.(1):

2)

The period of a simple pendulum is the time the pendulum takes to complete one oscillation. It is given by the formula

where

L is the length of the pendulum

g is the acceleration due to gravity at the location of the pendulum

Note that the period of a pendulum does not depend on its mass.

For the pendulum in this problem, we have:

L = 3 m is its length

is the acceleration due to gravity (calculated in part 1)

Therefore, the period of the pendulum is:

cant without the picture! ?