Two objects attract each other gravitationally with a force of 2.7×10−10 when they are 0.65 apart. Their total mass is 4.4 Find their individual masses.

To find the individual masses of the two objects, we can use Newton's law of universal gravitation, which states that the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

The formula for Newton's law of universal gravitation is:

F = G * ( m1 * m2 ) / r^2

Where:
- F is the gravitational force between the two objects,
- G is the gravitational constant (approximately 6.67430 × 10^−11 N m^2/kg^2),
- m1 and m2 are the masses of the two objects, and
- r is the distance between the centers of the two objects.

We know:
- F = 2.7 × 10^−10 N (given)
- r = 0.65 m (given)
- G = 6.67430 × 10^−11 N m^2/kg^2 (constant)

Now, let's plug in the values and solve for the individual masses:

2.7 × 10^−10 N = ( 6.67430 × 10^−11 N m^2/kg^2 ) * ( m1 * m2 ) / ( 0.65 m )^2

Simplifying further:

2.7 × 10^−10 N = ( 6.67430 × 10^−11 N m^2/kg^2 ) * ( m1 * m2 ) / 0.4225 m^2

Cross multiplying:

( 6.67430 × 10^−11 N m^2/kg^2 ) * ( m1 * m2 ) = 2.7 × 10^−10 N * 0.4225 m^2

Dividing both sides by ( 6.67430 × 10^−11 N m^2/kg^2 ):

m1 * m2 = ( 2.7 × 10^−10 N * 0.4225 m^2 ) / ( 6.67430 × 10^−11 N m^2/kg^2 )

m1 * m2 = 0.011415 kg^2

Now, we need to find two numbers whose product is 0.011415 kg^2 and whose sum is 4.4 kg (given total mass).

Since the individual masses are most likely in a ratio, let's assume one of the masses as 'x' (in kg). Therefore, the other mass would be '4.4 - x' (in kg).

x * (4.4 - x) = 0.011415 kg^2

Expanding:

4.4x - x^2 = 0.011415 kg^2

Rearranging the equation:

x^2 - 4.4x + 0.011415 kg^2 = 0

Now, we can solve this quadratic equation to find the values of 'x' (one of the individual masses).