Question

The ratio of work done by the internal forces of a car in order to change its speed from 0 to V and from
V to 2V is (Assume that the car moves on a horizontal road) -
(A) 1
(B) 1/2
(C) 1/3
(D) 1/4​

Answer 1

Answer:

1. 1/2 here is your answer

Answer 2

Answer:

The ratio of work done by the internal forces of a car is 1/3 i.e.option (C).

Explanation:

The work done can be calculated as,

$\mathrm{W=\frac{1}{2}m\Delta v^2 }$                (1)

Where,

W=work done by the internal force

m=mass of the body

Δv=change in velocity

CASE I: Speed changes from 0 to V

The initial velocity(v₁)=0 m/s

The final velocity(v₂)=V m/s

By inserting the value of final and initial velocity in equation (1) we get;

$\mathrm{W_1=\frac{1}{2}m(V-0)^2 }$

$\mathrm{W_1=\frac{1}{2}mV^2 }$           (2)

CASE II: Speed changes from V to 2V

The initial velocity(v₁)=V m/s

The final velocity(v₂)=2V m/s

By inserting the value of final and initial velocity in equation (1) we get;

$\mathrm{W_2=\frac{1}{2}m((2V)^2-(V)^2) }$

$\mathrm{W_2=\frac{1}{2}m(4V^2-V^2) }$

$\mathrm{W_2=\frac{3}{2}mV^2 }$          (3)

By taking the ratio of equations (2) and (3) we get;

$\mathrm{\frac{W_1}{W_2}=\frac{\frac{1}{2}mV^2 }{\frac{3}{2}mV^2 }}$

$\mathrm{\frac{W_1}{W_2}=\frac{1}{3} }$

So, the ratio of work done by the internal forces of a car is 1:3 i.e.option (C).

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