Gravitational force of attraction “F” exists between two point masses A and B when a fixed distance separates them. After mass A is doubled and mass B is quartered, the gravitational attraction between the two masses is
1/4 of the original force.
To determine the new gravitational attraction between the two masses, we need to use Newton's law of universal gravitation:
F = (G * m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant (approximately 6.67430 x 10^-11 N m^2 / kg^2), m1 and m2 are the masses of the two objects, and r is the distance between them.
Let's denote the initial masses of A and B as m1 and m2 respectively, and the initial gravitational force as F1. After mass A is doubled and mass B is quartered, the new masses become 2m1 and m2/4.
Now we can calculate the new gravitational force F2 using the updated masses:
F2 = (G * (2m1) * (m2/4)) / r^2
Simplifying this equation, we get:
F2 = (1/2) * F1
Therefore, the new gravitational attraction between the two masses is half (1/2) of the initial gravitational attraction.
To calculate the new gravitational attraction between the two masses after mass A is doubled and mass B is quartered, we need to use the formula for gravitational force:
F = G * (m1 * m2) / r^2
where:
F is the gravitational attraction
G is the gravitational constant (approximately 6.674 × 10^-11 N(m/kg)^2)
m1 and m2 are the masses of the two point masses
r is the distance between the two point masses
Let's assume the original masses of A and B are m1 and m2 respectively, and the original gravitational attraction is F1.
Original gravitational attraction: F1 = G * (m1 * m2) / r^2
After mass A is doubled, the new mass of A becomes 2m1. After mass B is quartered, the new mass of B becomes 1/4 * m2.
New gravitational attraction: F2 = G * ((2m1) * (1/4m2)) / r^2
Simplifying:
F2 = G * (2m1 * 1/4m2) / r^2
F2 = G * (2/4) * (m1/m2) / r^2
F2 = G * (1/2) * (m1/m2) / r^2
Therefore, the new gravitational attraction between the two masses is equal to half of the original gravitational attraction:
F2 = (1/2) * F1