Question

1. Calculate the new gravitational force between A and B if the mass of object A is doubled and distance R doubles

Answer 1

1) The new gravitational force is half of the original force

2) The new gravitational force is 1/8 of the original force

Explanation:

1)

Let's call F the initial gravitational force between the object A and B. The magnitude of F is given by the equation

The magnitude of the gravitational force between two objects is given by

$F=G\frac{m_A m_B}{R^2}$

where

$G=6.67\cdot 10^{-11} m^3 kg^{-1}s^{-2}$ is the gravitational constant

$m_A,m_B$ are the masses of the two objects

R is the separation between them

In this part of the problem, we are told that the distance between the two objects doubles, so the new distance is

R' = 2R

While the mass of object A is doubled, so the new mass is

$m_A' = 2m_A$

Therefore, the new gravitational force is

$F' = \frac{Gm_A' m_B}{R'^2}= \frac{G(2m_A) m_B}{(2R)^2}=\frac{1}{2}(\frac{Gm_A m_B}{R^2})=\frac{F}{2}$

Therefore, the new force is half of the original force.

2)

In this second part of the problem, the distance between the two objects doubles, so the new distance is

R' = 2R

While the mass of object A is halved, so the new mass is

$m_A' = \frac{m_A}{2}$

Therefore, the new gravitational force this time is:

$F' = \frac{Gm_A' m_B}{R'^2}= \frac{G(m_A/2) m_B}{(2R)^2}=\frac{1}{8}(\frac{Gm_A m_B}{R^2})=\frac{F}{8}$

Therefore, the new force is 1/8 of the original force.

Learn more about gravitational force:

brainly.com/question/1724648

brainly.com/question/12785992

#LearnwithBrainly