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# Calculate the magnitude of force which when applied on a body of mass $0.5kg$ produces an acceleration of $5m{s^{ - 2}}$.A. $2.8N$B. $2.5N$C. $5N$D. $10N$

Last updated date: 16th Jul 2024
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Hint:While Newton’s laws of motion may seem obvious to us today, centuries ago they were considered revolutionary. The three laws of motion help us understand how objects behave when they are standing still, when moving and when forces act upon them.Newton’s second law of motion gives the definition of force and all the applications related to force. This definition of force is used in all the problems of mechanics.

Mechanics is a branch of physics that deals with motion and the dynamics of its working. Sir Isaac Newton was the creator of this branch. He gave three laws of motion.Newton’s First Law of Motion states that a body in uniform motion will stay in uniform motion and a body in rest will stay in rest unless an external force is applied on the body.

Newton’s Second Law of Motion states that the acceleration of a body is directly related to the net force and inversely related to mass.Newton’s Third Law of motion states that every action has an equal and opposite reaction.Now according to second law of motion,
$a \propto F$, and
$a \propto \dfrac{1}{m}$
So,
$a \propto \dfrac{F}{m}$, here after eliminating the proportionality sign, the constant used is
$1$.
So,
$a = \dfrac{F}{m}$
$\Rightarrow F = ma$
Where, $F =$External force applied,$m =$Mass of body$= 0.5kg$ and $a =$Acceleration of body$= 5m{s^{ - 2}}$.
So,
$F = 0.5 \times 5$
$\therefore F = 2.5N$

Therefore the correct answer is option B.

Note:Force is also defined as the rate of change of momentum with respect to time. Which means that force is equal to the ratio of change in momentum and time taken for that change to occur. This change in momentum causes the occurrence of acceleration in the body. That acceleration can be uniform or non-uniform. All this Newtonian mechanics is applicable only if the frame of reference is either at rest or in uniform motion. If the frame of reference is in accelerated motion, these laws fail.