Three balls A, B and C are kept in a straight line. The separation between A and C is 1 m, and B is placed at the midpoint between them. The masses of A, B, C are 100 g, 200 g and 300 g respectively. Find the net gravitational force on (a) A, (b) B, and (c) C.
To find the net gravitational force on each ball, we need to calculate the gravitational force between each pair of balls and then add them up.
First, let's calculate the gravitational force between A and B.
The formula to calculate the gravitational force between two objects is given by Newton's law of gravitation:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force between the objects,
G is the gravitational constant (approximately equal to 6.674 × 10^-11 N(m/kg)^2),
m1 and m2 are the masses of the two objects, and
r is the distance between the centers of the two objects.
In this case, the mass of ball A is 100 g (0.1 kg), the mass of ball B is 200 g (0.2 kg), and the distance between their centers is 0.5 m (half the separation between A and C).
Using the formula, we can calculate the gravitational force between A and B:
F_AB = (G * m1 * m2) / r^2
= (6.674 × 10^-11 N(m/kg)^2 * 0.1 kg * 0.2 kg) / (0.5 m)^2
Simplifying this calculation will give us the gravitational force between A and B.
Next, let's calculate the gravitational force between B and C.
The mass of ball B is 200 g (0.2 kg), the mass of ball C is 300 g (0.3 kg), and the distance between their centers is also 0.5 m.
Using the same formula as before, we can calculate the gravitational force between B and C.
F_BC = (G * m1 * m2) / r^2
= (6.674 × 10^-11 N(m/kg)^2 * 0.2 kg * 0.3 kg) / (0.5 m)^2
Finally, to find the net gravitational force on each ball, we need to sum up the forces.
(a) For ball A, the net gravitational force will be F_AB.
(b) For ball B, the net gravitational force will be the sum of F_AB and F_BC.
(c) For ball C, the net gravitational force will be F_BC.
Calculate the above values using the given masses and separation, and you will get the net gravitational force on each ball.