Two cars having masses in the ratio $4:5$, accelerate in the ratio $2:3$. Find the ratio of forces exerted by each of them.

As given in the question, two cars having masses in the ratio of $4:5$, accelerate in the ratio $2:3$. 

Let the mass of the first car $m_1=4m$

Mass of the second car $m_2=5m$

Acceleration in the first car $a_1=2a$

Acceleration in the second car $a_2=3a$

Therefore, force exerted by first car, $F_1=m_1a_1=4m\times 2a=8ma$

Force exerted by the second car, $F_2=m_2a_2=5m\times3a=15ma$

Therefore, the ratio of the exerted forces by the two cars $=F_1:F_2=8ma:15ma=8:15$

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Updated on: 10-Oct-2022

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