Question

A certain simple pendulum has a period on the earth of 1.70s . What is its period on the surface of Mars, where g=3.71m/s^2?

Answer 1

The period of a simple pendulum on Mars can be calculated using the equation T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity. By substituting the given Earth period and Mars acceleration due to gravity into the equation, we can find the period on Mars.

Step-by-step explanation:

The period of a simple pendulum is given by the equation:

T = 2π√(L/g)

Where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity. If the period on Earth is 1.70s and the acceleration due to gravity on Mars is 3.71m/s^2, we can calculate the period on Mars as:

T_mars = 2π√(L/3.71)

By substituting the given Earth period of 1.70s into the equation, we can solve for the length of the pendulum, and then substitute this length into the equation for Mars to find the period on Mars.

Calculating these values, we find:

L = (T^2 x g)/(4π^2)

L = (1.70^2 x 9.81)/(4π^2)

L ≈ 1.16 meters

Substituting this length into the equation for Mars:

T_mars = 2π√(1.16/3.71)

T_mars ≈ 2.48s

Answer 2

To calculate the period of a pendulum on Mars, use the ratio of the gravitational acceleration values of Earth and Mars and the known period on Earth. The new period is found by multiplying the Earth period by the square root of the ratio of Earth's gravity to Mars' gravity.

Step-by-step explanation:

To determine the period of a pendulum on Mars, given that it has a period of 1.70 seconds on Earth, we can use the formula for the period (T) of a simple pendulum:
T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity.

The question gives us g on Earth as 9.81 m/s² and on Mars as 3.71 m/s². Since the period is proportional to the square root of 1/g, we can find the ratio of the periods on Earth and Mars using the ratio of the acceleration due to gravity:

Ratio = √(gEarth/gMars)

Thus, the new period on Mars (TMars) can be found with:

TMars = TEarth × Ratio

Substituting the given values, we get:
TMars = 1.70 s × √(9.81 m/s² / 3.71 m/s²)

After calculating the above expression, you will get the new period of the pendulum on Mars.