If the gravitational force between two objects of masses 10kg each is 50N. What will be the new gravitational force if the distance between the objects is reduced to 1/3rd of the original distance and the mass of one object is doubled?
The gravitational force between two objects is given by the equation F = (G * m1 * m2) / r^2, where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between the objects.
In this case, we are given:
m1 = m2 = 10 kg (mass of each object)
F = 50 N (gravitational force)
r = original distance between the objects
To find the new gravitational force, we need to determine the new distance and the new mass of one object.
Given that the distance between the objects is reduced to 1/3rd of the original distance, the new distance would be r/3.
Given that the mass of one object is doubled, the new mass would be 2 * m1.
Using these values, the new gravitational force (F') can be calculated as follows:
F' = (G * (2 * m1) * m2) / (r/3)^2
Substituting the given values:
F' = (G * (2 * 10 kg) * 10 kg) / (r/3)^2
Now, we can simplify the equation:
F' = (G * 20 kg * 10 kg) / (r/3)^2
To determine the new gravitational force, we need to know the value of the gravitational constant G. However, since this value is not provided in the question, we cannot calculate the exact value of the new gravitational force.
To find the new gravitational force, we can use Newton's law of universal gravitation. The formula is as follows:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force between the two objects
G is the gravitational constant (approximately 6.674 * 10^-11 N*m^2/kg^2)
m1 and m2 are the masses of the two objects
r is the distance between the centers of the two objects
In this case, we have the following information:
m1 = 10 kg
m2 = 10 kg (since both objects have the same mass initially)
F = 50 N
We need to calculate the new gravitational force when the distance is reduced to 1/3 and one of the masses is doubled.
Step 1: Find the original distance (r1) using the original gravitational force:
F = (G * m1 * m2) / r1^2
50 = (6.674 * 10^-11 * 10 * 10) / r1^2
Solving for r1, we get:
r1^2 = (6.674 * 10^-11 * 10 * 10) / 50
r1^2 = 2.6696 * 10^-11
r1 ≈ 5.1665 * 10^-6 meters
Step 2: Calculate the new distance (r2) by reducing the original distance to 1/3rd:
r2 = (1/3) * r1
r2 = (1/3) * 5.1665 * 10^-6
r2 ≈ 1.7222 * 10^-6 meters
Step 3: Calculate the new gravitational force (F2) when one of the masses is doubled and the distance is reduced:
F2 = (G * m1' * m2') / r2^2
m1' = 10 kg (one object has the same mass)
m2' = 2 * 10 = 20 kg (mass of one object is doubled)
Plugging in the values:
F2 = (6.674 * 10^-11 * 10 * 20) / (1.7222 * 10^-6)^2
Simplifying this equation will give us the final answer.
To find the new gravitational force, you need to consider the changes in distance and mass.
1. Change in distance: The new distance between the objects is reduced to 1/3 of the original distance.
Let's denote the original distance as d. The new distance is then (1/3) * d.
2. Change in mass: The mass of one of the objects is doubled. Let's denote the original mass of each object as m. The new mass of one object is then 2m.
Now, let's calculate the new gravitational force using Newton's law of universal gravitation:
Original gravitational force: F = G * (m1 * m2) / (d^2)
New gravitational force: F' = G * (m1' * m2') / ((1/3)^2 * d^2)
Substituting the changes in mass and distance:
F' = G * (2m * m) / (1/9 * d^2)
Simplifying further:
F' = 18 * G * m^2 / d^2
So, the new gravitational force will be 18 times the original gravitational force. Given that the original force is 50N, the new gravitational force would be:
F' = 18 * 50N = 900N