Question

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.

Answer 1

Question : -

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.

ANSWER

Given : -

Ratio of their masses = 4 : 5

Ratio of their acceleration = 2 :3

Required to find : -

• Ratio of forces exerted by each of them ?

Solution : -

Let,

The two cars be car-1 & car-2 ! respectively ..

Mass of car-1 be m1

Mass of car-2 be m2

Ratio of their Masses = 4 : 5

This implies;

m1 : m2 = 4 : 5

• => m1 = 4x
• => m2 = 5x

Similarly,

Acceleration of car-1 be a1

Acceleration of car-2 be a2

Ratio of their acceleration = 2 : 3

This implies;

a1 : a2 = 2 : 3

• => a1 = 2y
• => a2 = 3y

Here, we know that

• Force = Mass x Acceleration (F = ma)

So,

Force exerted by car-1 (F1) = m1 x a1

= 4x * 2y

= 8xy

Similarly,

Force exerted by car-2 (F2) = m2 x a2

= 5x * 3y

= 15xy

Now,

Ratio of forces exerted by each of them = F1 : F2

F1 : F2 = 8xy : 15xy

F1 : F2 = 8 : 15

Therefore,

Ratio of forces exerted by each of them = 8 : 15

Answer 2

Given :-

• Ratio of mass of the car = 4:5
• Ratio of the acceleration = 2:3

To Find :-

• Ratio of forces exerted by each of them.

Solution :-

• Let the masses be $\sf{m_1}$ and $\sf{m_2}$ .
• Let the Accelerations be $\sf{a_1}$ and $\sf{a_2}$
• Let the forces be $\sf{f_1}$ and $\sf{f_2}$.

We know that,

$\red\bigstar\:\:\:\boxed{\underline{{\sf\blue {Force = Mass \times Accelaration }}}}$

So,

Force exerted by car-1 :-

$\dashrightarrow\:\:\:\sf{ F_1 = m_1 \times a_1}$

$\dashrightarrow\:\:\:\sf{ F_1 = 4x \times 2y}$

$\dashrightarrow\:\:\:\sf{ F_1 = 8xy}$

Force exerted by car-2 :-

$\dashrightarrow\:\:\:\sf{ F_2 = m_2\times a_2}$

$\dashrightarrow\:\:\:\sf{ F_2 = 5x \times 3y}$

$\dashrightarrow\:\:\:\sf{ F_2 = 15xy}$

Ratio of forces exerted by each of them :-

$\dashrightarrow\:\:\:\sf{ F_1 : F_2}$

$\dashrightarrow\:\:\:\sf{ 8xy : 15xy}$

$\dashrightarrow\:\:\:\sf{ 8 : 15}$

∴  Ratio of forces exerted by each of them = 8 : 15