Question

1. a bear, cat, and ant are all at equal distance from each other. which pair has a higher gravitational force? (a) bear + ant (b) ant + cat (c) bear + cat (d) a and c are equal (e) all are equal 3. two rocks are floating in space 1 meter apart. the two rocks are suddenly pulled apart to 2 meters. explain the effect on the gravitational force between the rocks using the universal law of gravitation.

Explanation:

Step1: Recall the formula for gravitational force

The formula for gravitational force is \(F = G\frac{m_1m_2}{r^2}\), where \(G\) is the gravitational constant, \(m_1\) and \(m_2\) are the masses of the two objects, and \(r\) is the distance between them. In this case, the distance \(r\) is the same for all pairs. So the gravitational force depends only on the product of the masses (\(m_1m_2\)).

Step2: Compare the mass products of each pair

• For pair (A) Bear + Ant: Let the mass of the bear be \(m_{bear}\), mass of the ant be \(m_{ant}\). The product is \(m_{bear}\times m_{ant}\).
• For pair (B) Ant + Cat: Let the mass of the cat be \(m_{cat}\). The product is \(m_{ant}\times m_{cat}\).
• For pair (C) Bear + Cat: The product is \(m_{bear}\times m_{cat}\).

Since \(m_{bear}>m_{cat}>m_{ant}\), the product \(m_{bear}\times m_{cat}\) (pair C) is the largest.

Answer:

C. Bear + Cat