Question

A 2 kg laptop sits on the floor near a 4 kg jar of pennies. If the force of gravity

between them is 3.42 x 10-10 N, how far apart are they?
OA. 1.25 m
OB. 1.68 m
OC. 2.12 m
OD. 1.81 m

Answer 1

The distance between the laptop and the jar of pennies can be calculated using Newton's law of universal gravitation. The laptop and the jar of pennies are approximately 0.0546 meters apart.

Step-by-step explanation:

The force of gravity between two objects can be calculated using Newton's law of universal gravitation: F = G * (m1 * m2) / r^2, where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.

In this case, the force of gravity between the laptop and the jar of pennies is given as 3.42 x 10-10 N. The masses are 2 kg and 4 kg, respectively. Plugging these values into the formula, we can solve for the distance:

F = (6.67430 x 10-11 N m2/kg2) * (2 kg * 4 kg) / r^2

r^2 = (6.67430 x 10-11 N m2/kg2) * (2 kg * 4 kg) / (3.42 x 10-10 N)

r^2 = 0.002976

r = √(0.002976) = 0.0546 m

Therefore, the laptop and the jar of pennies are approximately 0.0546 meters or 5.46 cm apart.

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Answer 2

The distance between the laptop and the jar of pennies is approximately 1.0476 meters.

Step-by-step explanation:

The force of gravity between two objects can be calculated using Newton's Law of Universal Gravitation, which states that the force is directly proportional to the product of the masses and inversely proportional to the square of the distance between them.

In this case, we have a 2 kg laptop and a 4 kg jar of pennies with a force of gravity between them of 3.42 x 10-10 N. To find the distance between them, we can rearrange the formula to solve for distance:

F = (G * m1 * m2) / d2

Where F is the force of gravity, G is the gravitational constant (approximately equal to 6.674 x 10-11 N m2/kg2), m1 and m2 are the masses of the objects, and d is the distance between them.

Plugging in the values, we have:

3.42 x 10-10 N = (6.674 x 10-11 N m2/kg2) * (2 kg) * (4 kg) / d2

Simplifying the equation, we find:

d2 = (6.674 x 10-11 N m2/kg2) * (2 kg) * (4 kg) / (3.42 x 10-10 N)

d2 = 1.0957 m2

d = sqrt(1.0957) m

d ≈ 1.0476 m

Therefore, the distance between the laptop and the jar of pennies is approximately 1.0476 meters. None of the given options match this exact value, so the closest answer would be option OB. 1.68 m.