Question

What is the magnitude of the gravitational force exerted by a $15Kg$ mass on a $25Kg$ mass separated by a distance of $25cm$? What is the acceleration produced in each mass?

Answer 1

In order to solve this question, we are going to first see the given information, i.e. the two masses and their distance and then, by using the law of gravitation formula, the acceleration of the two bodies can be calculated by putting the values of masses and that of gravitational constant.

Formula used:
The acceleration of the first body can be calculated by using the formula for the law of Gravitation
$a = \dfrac{{Gm}}{{{d^2}}}$

Complete step-by-step answer:
It is given that the mass of the first body is ${m_1} = 15Kg$and the mass of the second body is ${m_2} = 25Kg$
Now, they are separated by a distance of $d = 25cm$
Now the acceleration of the first body can be calculated by using the formula for the law of Gravitation
${a_1} = \dfrac{{G{m_1}}}{{{d^2}}}$
Where $G = 6.674 \times {10^{ - 11}}$
Putting the values in this equation
${a_1} = \dfrac{{6.674 \times {{10}^{ - 11}} \times 15}}{{{{25}^2}}} = 2.67 \times {10^{ - 8}}m{s^{ - 2}}$
The acceleration for the second body can be calculated by using the formula
${a_2} = \dfrac{{G{m_2}}}{{{d^2}}}$
Putting these values in the equation
${a_2} = \dfrac{{6.674 \times {{10}^{ - 11}} \times 25}}{{{{25}^2}}} = 1.6 \times {10^{ - 8}}m{s^{ - 2}}$

Note: It is important to note that the accelerations of the two bodies are due to their masses and their positions as there are the gravitational forces that are acting between these two masses and that force depends on the masses of the bodies, their distance and the gravitational constant. The mass of the second body is more, so the acceleration is also more.