Question

A driver accelerates his car first at the rate of $1.8{m}/{{s}^{2}}$ and then at the rate of $1.2{m}/{{s}^{2}}$. The ratio of the forces exerted by the engines will be respectively equal to
A. 2:3
B. 1:2
C. 2:1
D. 3:2

Answer 1

Hint: To solve this question, use the formula for force in terms of mass and acceleration. Which is given as $F= m.a$. From this formula find the relationship between force and acceleration. Now, use this relationship and write the expression for the ratio of forces. Substitute the values of acceleration in this obtained expression and find the ratio of forces exerted by the engines.

Formula used:
$F= m.a$

Complete step-by-step solution:
Let ${a}_{1}$ and ${F}_{1}$ be the acceleration and force respectively when the driver accelerates his car for the first time.
${a}_{2}$ and ${F}_{2}$ be the acceleration and force respectively when the driver accelerates his car second time.
Given:
${a}_{1}= 1.8{m}/{{s}^{2}}$
${a}_{2}= 1.2{m}/{{s}^{2}}$
We know, force applied is given by,
$F= m.a$ …(1)
Where,
$m$ is the mass of the object
$a$ is the acceleration of the object
Here, mass of the object i.e. car remains constant. Thus, we can say force is directly proportional to the acceleration of the car. We can write it as,
$F \propto a$
Thus, we can write the ratio of forces as,
$\dfrac {{F}_{1}}{{F}_{2}}= \dfrac {{a}_{1}}{{a}_{2}}$
Substituting the given values in above expression we get,
$\dfrac {{F}_{1}}{{F}_{2}}= \dfrac {1.8}{1.2}$
$\Rightarrow \dfrac {{F}_{1}}{{F}_{2}}=\dfrac {3}{2}$
Thus, the ratio of the forces exerted by the engines will be respectively equal to 3:2.

So, the correct answer is option D i.e. 3:2.

Note:
We can solve this same problem by an alternate method. According to this method, use the formula for force applied in terms of mass and acceleration. Firstly, substitute the value of acceleration as $1.8{m}/{{s}^{2}}$ in the formula for force and calculate the value of force. Then, similarly, substitute the value of acceleration as $1.2{m}/{{s}^{2}}$ in the formula for force and calculate the value of force. Now, divide the obtained value of forces and obtain the ratio of the forces exerted by the engines.