Question

A pendulum that has a period of 3.00000 s and that is located where the acceleration due to gravity is 9.79 m/s² is moved to a location where the acceleration due to gravity is 9.82 m/s². What is its new period?

a) 2.982 s
b) 3.000 s
c) 3.018 s
d) 3.036 s

Answer 1

The new period of the pendulum is 3.018 s.

Step-by-step explanation:

The new period of the pendulum can be found using the relationship between the period and the acceleration due to gravity. The formula for the period of a pendulum is given by:

`T = 2\pi √(L/g)`

where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.

Given that the original period of the pendulum is 3.00000 s and the original acceleration due to gravity is 9.79 m/s², we can rearrange the formula to solve for L:

`L = (T/2\pi )^2 * g`

Substituting the values, we have:

`L = (3.0000/2\pi )^2* 9.79`

= 0.310 m

Now, we can use the new length and the new acceleration due to gravity (9.82 m/s²) in the formula for the period:

`T' = 2\pi √(L/g')`

=
`2\pi √(0.310/9.82)`

= 3.018 s

Therefore, the new period of the pendulum is 3.018 s.