Question

test information
description\tshow all you work, including units, on separate paper. follow the \problem solving method\.
\t\tthis final exam is cumulative and covers material from the entire course.
instructions\tfrom the list of choices, select the one best answer.
multiple attempts not allowed. this test can only be taken once.
force completion this test can be saved and resumed later.
\t\tyour answers are saved automatically.
question completion status:
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question 27 of 62
1.6 points save answer
question 27
the centers of two spheres, a and b, are 0.500 m apart. the masses of a and b are 450 kg and 985 kg, respectively. what is the magnitude of the gravitational force between these two spheres?
○ 3.12 × 10⁻⁴ n
○ 8.56 × 10⁻⁵ n
○ 1.18 × 10⁻⁴ n
○ 5.91 × 10⁻⁵ n

Explanation:

Step1: Recall Gravitational Force Formula

The formula for gravitational force between two objects is \( F = G\frac{m_1m_2}{r^2} \), where \( G = 6.674\times 10^{-11}\ \text{N}\cdot\text{m}^2/\text{kg}^2 \), \( m_1 \) and \( m_2 \) are the masses, and \( r \) is the distance between their centers.

Step2: Identify Given Values

Here, \( m_1 = 450\ \text{kg} \), \( m_2 = 985\ \text{kg} \), \( r = 0.500\ \text{m} \).

Step3: Substitute Values into Formula

First, calculate \( m_1m_2 = 450\times985 = 443250\ \text{kg}^2 \). Then, \( r^2=(0.500)^2 = 0.25\ \text{m}^2 \). Now, substitute into the formula: \( F = 6.674\times 10^{-11}\times\frac{443250}{0.25} \).

Step4: Perform the Calculation

Calculate \( \frac{443250}{0.25}=1773000 \). Then, \( F = 6.674\times 10^{-11}\times1773000 \). \( 6.674\times1773000 = 6.674\times1.773\times 10^{6}\approx11.83\times 10^{6}\times 10^{-11}=11.83\times 10^{-5}=1.183\times 10^{-4}\ \text{N} \), which is approximately \( 1.18\times 10^{-4}\ \text{N} \).

Answer:

\( 1.18\times 10^{-4}\ \text{N} \) (corresponding to the option with this value)