Question

How does the acceleration $\left( a \right)$ produced by a given force $\left( F \right)$depend on the mass $\left( m \right)$of the body?
(A) $F = \dfrac{m}{g}$
(B) $F = mg$
(C) $F = ma$
(D) $F = \dfrac{m}{a}$

Answer 1

Hint
From Newton's second law of motion, we see that the force that is applied on a body is given by the product of the mass of the body and the acceleration that is caused on the body due to that force. Hence, the acceleration produced by a given force depends on mass as: $F = ma$.

Complete step by step answer
From Newton's second law of motion a mass acquires acceleration when a force is applied to it. The value of the acceleration that is produced in the body is directly proportional to the force on the body and is inversely proportional to the mass of the body. This means that if force is applied to two bodies then the acceleration produced in them varies inversely with their masses. Therefore, we can write that the force that is applied on a body is the product of the mass and the acceleration that is produced in the body due to the force. So we can write,
$\Rightarrow F = ma$
where $m$ is the mass of the body and $a$ is the acceleration of the body.
Hence the correct answer is given by option (C).

Note
Newton's second law of motion states that the acceleration in an object produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force and inversely proportional to the mass of the object. The unit of force is given by the product of the units of mass and acceleration, which is $kgm/{s^2}$. This unit is termed as Newton and is denoted by N. The dimensions of force are $\left[ {{M^1}{L^1}{T^{ - 2}}} \right]$.