Question

We have two masses \[{{m}_{1}}\] and \[m_2\] separated by distance $d$. Now if the mass \[{{m}_{2}}\] is reduced to 50% and the force exerted by \[{{m}_{1}}\] on \[{{m}_{2}}\] is 20 N, what is the force exerted by \[{{m}_{2}}\] on \[{{m}_{1}}\]?

Answer 1

Hint: We know from universal law of gravitation that any two bodies in the universe exert force on each other which is directly proportional to the masses of the two bodies and inversely proportional to the square of distance between them. Since the bodies given in the question are not charged, so the force is the gravitational force.

Complete answer:
The concept of force had its origin in Newton’s second law. According to the second law force is equal to the rate of change of momentum. In simple words we can define it as the product of mass and acceleration produced in the body.
Initially the separation between the two bodies was d. after some time the mass of the second body is reduced to 50%. After this reduction the force exerted by \[{{m}_{1}}\] on \[{{m}_{2}}\] is 20N and we need to find the force exerted by \[{{m}_{2}}\] on \[{{m}_{1}}\]. We know according to Newton’s third law; forces always occur in pairs. So this implies that if the force exerted by \[{{m}_{1}}\] on \[{{m}_{2}}\] is 20 N, then the force exerted by \[{{m}_{2}}\] on \[{{m}_{1}}\] will also be 20 N.
 So, the answer is 20 N.

Note:
According to Newton’s third law, forces always occur in pairs. A single force cannot exist in the universe. when some forces are acting on a body then the resultant force is given by adding them vectorially. Also, we could have found the answer by using universal law of gravitation but that would have been cumbersome and time taking.