(a) Newton's first law of motion gives a qualitative definition of force. Justify.
(b) Which would require a greater force for accelerating - a $2 k g$ of mass at $4 {m s}^{- 2}$ or a $3 k g$ of mass at $2 {m s}^{- 2}$ ?

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Solution

(a) An object remains in the state of rest or of uniform motion in a straight line unless compelled to change that state by an applied unbalanced force.
All objects resist a change in their state of motion. The tendency of undisturbed objects to stay at rest or to keep moving with the same velocity is called inertia. This is why, the first law of motion is also known are the law of inertia. Here, the state of an object is changed only when an external force acts on it. This it provides a qualitative definition of force.

(b) Force, $F = m a$
Given, $m_{1} = 2 k g, a_{1} = 4 {m s}^{- 2}$
$m_{2} = 3 k g; a_{2} = 2 {m s}^{- 2}$
Thus, $F_{1} = m_{1} a_{1} = 2 k g \times 4 {m s}^{- 2} = 8 N$
$F_{2} = m_{2} a_{2} = 3 k g \times 2 {m s}^{- 2} = 6 N$
$∴$ $F_{1} > F_{2}$
Thus, accelerating a $2 k g$ mass at $4 {m s}^{- 2}$ would require a greater force.

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