The distance between the midponts of two metal balls.P and Q,respectively of masses 55 kg and 70 kg is 80 cm

calculate the gravitational force that P exerts on Q
answer
F=Gm1m2/r^2
F=(6,67x10^-11)(55kg)(70kg)/(80cm)
F=4.01x10^-11..... Is it correct is correct
(b)give only the magnitude of the force that Q exerts on P
(c)if Q Is now replaced by a ball that 1/2 its original mass and the distance between the balls is doubled.determine the New force.

(a) To calculate the gravitational force that P exerts on Q, we can use the formula F = G * m1 * m2 / r^2, where F represents the gravitational force between the two objects, G is the gravitational constant (approximately 6.67 × 10^-11 Nm^2/kg^2), m1 is the mass of object P (55 kg), m2 is the mass of object Q (70 kg), and r is the distance between the midpoint of the two objects (80 cm = 0.8 m).

Plugging in the values into the formula, we get:
F = (6.67 × 10^-11 Nm^2/kg^2) * (55 kg) * (70 kg) / (0.8 m)^2
F ≈ 4.56 × 10^-10 N

So the gravitational force that P exerts on Q is approximately 4.56 × 10^-10 N.

(b) To find the magnitude of the force that Q exerts on P, we can use Newton's third law of motion which states that the force between two objects is equal in magnitude but opposite in direction. Therefore, the magnitude of the force that Q exerts on P will be the same as the magnitude of the force that P exerts on Q, which we calculated in part (a) as approximately 4.56 × 10^-10 N.

(c) If Q is replaced by a ball that is 1/2 its original mass, the mass of Q will be 70 kg / 2 = 35 kg. If the distance between the balls is doubled, the new distance (r') will be 2 * r = 2 * 0.8 m = 1.6 m.

To determine the new force between the balls, we can use the same formula as before:
F' = G * m1 * m2 / r'^2
F' = (6.67 × 10^-11 Nm^2/kg^2) * (55 kg) * (35 kg) / (1.6 m)^2
F' ≈ 3.26 × 10^-10 N

So the new force between the balls, when Q is replaced by a ball that is 1/2 its original mass and the distance between the balls is doubled, is approximately 3.26 × 10^-10 N.

To calculate the gravitational force between two objects, we can 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 6.67 x 10^-11 Nm^2/kg^2),
m1 and m2 are the masses of the objects, and
r is the distance between the centers of the objects.

Let's solve the given questions step by step:

(a) Calculating the gravitational force that P exerts on Q:
Using the given values:
m1 = 55 kg (mass of P)
m2 = 70 kg (mass of Q)
r = 80 cm = 0.8 m (distance between the midpoints)

Plugging these values into the formula, we get:
F = (6.67 x 10^-11 Nm^2/kg^2) * (55 kg) * (70 kg) / (0.8 m)^2

Simplifying the equation, we get:
F ≈ 4.01 x 10^-11 N

So, the gravitational force that P exerts on Q is approximately 4.01 x 10^-11 N.

(b) The magnitude of the force that Q exerts on P is the same as the force that P exerts on Q. So, the magnitude is also 4.01 x 10^-11 N.

(c) If Q is replaced by a ball that is half its original mass (35 kg), and the distance between the balls is doubled (r = 2 * 0.8 m = 1.6 m), we can calculate the new force.

Using the same formula as before:
F = (6.67 x 10^-11 Nm^2/kg^2) * (55 kg) * (35 kg) / (1.6 m)^2

Simplifying the equation, we get:
F ≈ 6.95 x 10^-12 N

So, the new force between the balls is approximately 6.95 x 10^-12 N.