Question

Two cars having masses in the ratio 5 : 6, accelerate in the ratio 3:4. Find the ratio of forces exerted by each of them.
A) 5:16 B) 5:8 C) 3:8 D) 3:5​

Answer 1

AnswEr:

option (B)  5 : 8

ExplanaTion:

Let, masses of two Cars 1 an 2 be

m₁ = 5 y

m₂ = 6 y  

and,

Acceleration of two Cars 1 and 2 be

a₁ = 3 z

a₂ = 4 z

then,

Using formula to calculate force

Force = mass × acceleration

●Calculating force exerted by Car 1

Let , force exerted by Car 1 = F₁

then,

→   F₁ = m₁ × a₁

→   F₁ = 5 y × 3 z

→   F₁ = 15 y z  ..... equation (1)

● Calculating force exerted by Car 2

Let force exerted by Car 2 = F₂

then,

→   F₂ = m₂ × a₂

→   F₂ = 6 y × 4 z

→ F₂ = 24 y z  ...... equation (2)

Now,

● Calculating the ratio between force exerted by each of them

→   F₁ : F₂

(using equation (1) and (2) )

→   F₁ : F₂ = (15 y z) / (24 y z)

→   F₁ : F₂ = 15 / 24

→   F₁ : F₂ = 5 / 8  

→   F₁ : F₂ = 5 : 8

Therefore,

Ratio between the forces exerted by each of them is 5 : 8 .