Question

Two cars of masses m₁ and m₂ are moving with the same kinetic energy. The mass m₁ is more than the m₂. If both the cars have equal retardation when the brakes are applied then the distance covered by both the cars are S₁ and S₂ respectively, before coming to rest. Then:
1. S₁ = S₂
2. S1 < S2
3. S1 > S2
4. S1 = 2S2

Answer 1

Correct Answer - Option 2 : S1 < S2

CONCEPT:

Kinetic Energy

• The energy possessed by a particle by the virtue of its motion is called kinetic energy. It is given by,

​\(⇒ KE=\frac{1}{2}m× v^{2}\)  

Where KE = kinetic energy, m = mass and v = velocity

CALCULATION:

Given \(m_{1}>m_{2}\), a₁ = a₂ = a (retardation)

• The kinetic energy of a body is given as,

\(⇒ KE=\frac{1}{2}m× v^{2}\)     -----(1)

• Both the cars have equal kinetic energy,

\(\Rightarrow KE_{1}=KE_{2}=KE\)     -----(2)

• For the car of mass m₁,

\(⇒ KE=\frac{1}{2}m_{1}× v_{1}^{2}\)     -----(3)

• For the car of mass m2,

\(⇒ KE=\frac{1}{2}m_{2}× v_{2}^{2}\)     -----(4)

By equation 3 and equation 4,

\(⇒ m_{1}× v_{1}^{2}=m_{2}× v_{2}^{2}\)

\(\Rightarrow \frac{v_{1}^{2}}{v_{2}^{2}}=\frac{m_{2}}{m_{1}}\)     -----(5)

\(\Rightarrow v_{1}<v_{2}\)    

• The third equation of motion is given as,

\(\Rightarrow v^{2}=u^{2}+2aS\)

• For mass m₁,

\(\Rightarrow 0^{2}=v_{1}^{2}-2aS_{1}\)

\(\Rightarrow S_{1}=\frac{v_{1}^{2}}{2a}\)     -----(6)

• For mass m2,

\(\Rightarrow 0^{2}=v_{2}^{2}-2aS_{2}\)

\(\Rightarrow S_{2}=\frac{v_{2}^{2}}{2a}\)     -----(7)

By equation 6 and equation 7,

\(\Rightarrow \frac{S_{1}}{S_{2}}=\frac{v_{1}^{2}}{v_{2}^{2}}\)     -----(8)

By equation 5 and equation 8,

\(\Rightarrow S_{1}<S_{2}\)

• Hence, option 2 is correct.