Question

select the correct answer.
the weight of an object on earth is 350 newtons. on mars, the same object would weigh 134 newtons. what is the acceleration due to gravity on the surface of mars, given that it is 9.8 meters/second² on earth?
a. 0.78 meters/second²
b. 2.74 meters/second²
c. 3.75 meters/second²
d. 5.78 meters/second²
e. 9.80 meters/second²

Explanation:

Step1: Recall the formula for weight

Weight \( W \) is given by the formula \( W = m \times g \), where \( m \) is mass and \( g \) is acceleration due to gravity. The mass of the object remains constant on Earth and Mars. So, first, find the mass of the object using Earth's weight and gravity.
On Earth, \( W_{Earth} = 350 \, \text{N} \) and \( g_{Earth} = 9.8 \, \text{m/s}^2 \). From \( W = m \times g \), we can solve for mass \( m \): \( m=\frac{W_{Earth}}{g_{Earth}} \).
Substituting the values: \( m = \frac{350}{9.8} \approx 35.714 \, \text{kg} \).

Step2: Calculate Mars' gravity

On Mars, the weight \( W_{Mars} = 134 \, \text{N} \) and the mass \( m \) is the same as on Earth (≈35.714 kg). Using the weight formula again \( W = m \times g \), we can solve for \( g_{Mars} \): \( g_{Mars}=\frac{W_{Mars}}{m} \).
Substituting the values: \( g_{Mars}=\frac{134}{35.714} \approx 3.75 \, \text{m/s}^2 \).

Answer:

C. 3.75 meters/second²