Question

The vector form of the universal law of gravitation:

• A. \( \vec{F} = \frac{G m_1 m_2}{r^2} \hat{r} \)
• B. \( \vec{F} = \frac{G m_1 m_2}{r^3} \hat{r} \)
• C. \( \vec{F} = \frac{G m_1 m_2}{r^2} \)
• D. \( \vec{F} = \frac{G m_1 m_2}{r^3} \hat{r} \)

Hint:

Remember, the vector form of the universal law of gravitation accounts for both the magnitude and direction of the force. The direction is given by the unit vector \( \hat{r} \), which points from one mass to the other.

Answer 1

The Correct Option is D

Step 1: Understand the universal law of gravitation.
The universal law of gravitation states that the gravitational force \( \vec{F} \) between two masses \( m_1 \) and \( m_2 \) is directly proportional to the product of the masses and inversely proportional to the square of the distance between them: \[ F = \frac{G m_1 m_2}{r^2} \] Where:
\( G \) is the gravitational constant,
\( m_1 \) and \( m_2 \) are the masses of the two objects,
\( r \) is the distance between the centers of the two masses.

Step 2: Convert the formula into vector form.
Since the force is a vector, the direction of the force must also be considered. The force is directed along the line joining the two masses, which is given by the unit vector \( \hat{r} \). Thus, the vector form of the law is: \[ \vec{F} = \frac{G m_1 m_2}{r^3} \hat{r} \] Where \( \hat{r} \) is the unit vector pointing from one mass to the other. % Correct Answer Correct Answer:} (4) \( \vec{F} = \frac{G m_1 m_2}{r^3} \hat{r} \)