Two bodies with masses m1 = 4 kg and m2 = unknown kg, are at a distance r = 2 m from each other

Two bodies with masses m1 = 4 kg and m2 = unknown kg, are at a distance r = 2 m from each other and are attracted with a force of 1.3 • 10-10. Determine the value of the quantity denoting the unknown.

Given:

m1 = 4 kilograms – the mass of the first body;

r = 2 meters – distance between bodies;

G = 6.67 * 10 ^ -11 N * kg2 / m2 – gravitational constant;

F = 1.3 * 10 ^ -10 Newton – the force of gravitational interaction of bodies.

It is required to determine m2 (kilogram) – the mass of the second body.

To determine the mass of the second body, you must use the following formula:

F = G * m1 * m2 / r ^ 2, from here we find that:

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

m2 = 1.3 * 10 ^ -10 * 2 ^ 2 / (6.67 * 10 ^ -11 * 4) = 1.3 * 10 ^ -10 / (6.67 * 10 ^ -11) =

= 1.3 * 10 / 6.67 = 13 / 6.67 = 1.9 kilograms (the result has been rounded to one decimal place).

Answer: the mass of the second body is 1.9 kilograms.