the gravitational force between two objects is ____ proportional to the product of the masses of the objects

Physics

1 answer:

OLEGan [10]3 years ago

6 0

Explanation:

There exist a force of gravity between two masses. It is given by :

$F=G\times \dfrac{m_1m_2}{r^2}$ ...........(1)

Where

G is the universal gravitational constant

m₁ and m₂ are masses

r is the distance between them

From equation (1) it is clear that the force of gravity between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

So, the gravitational force between two objects is directly proportional to the product of the masses of the objects

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Answer:

The magnitude of the resultant decreases from A+B to A-B

Explanation:

The magnitude of the resultant of two vectors is given by

$R=\sqrt{A^2 +B^2 +2AB cos \theta}$

where

A is the magnitude of the first vector

B is the magnitude of the second vector

$\theta$ is the angle between the directions of the two vectors

In the formula, A and B are constant, so the behaviour depends only on the function $cos \theta$ . The value of $cos \theta$ are:

- 1 (maximum) when the angle is 0, so the magnitude of the resultant in this case is

$R=\sqrt{A^2 +B^2+2AB}=\sqrt{(A+B)^2}=A+B$

- then it decreases, until it becomes 0 when the angle is 90 degrees, where the magnitude of the resultant is

$R=\sqrt{A^2 +B^2+0}=\sqrt{A^2+B^2}$

- then it becomes negative, and continues to decrease, until it reaches a value of -1 when the angle is 180 degrees, and the magnitude of the resultant is

$R=\sqrt{A^2 +B^2-2AB}=\sqrt{(A-B)^2}=A-B$