JEE Main 1-Sep-2021 Shift 2 Solved Paper

Given, the length of the shock absorber, I = 1.5 m
The total mass of the system, M = 40000 kg
The speed of the wagon, v = 72 km/h
When brakes are applied, the final velocity, vf = 0
The compressed spring of the shock absorber, x = 1mApplying the work-energy theorem,
Work done by the system = Change in kinetic energy
W = Δ KE
Wfriction+Wspring=

1

2

mvf2+

1

2

mvi2
−

90

100

(

1

2

mv2)+Wspring=0−

1

2

mvi2 (∵ 90% energy lost due to friction)
Wspring=−

10

100

×

1

2

mv2
−

1

2

kx2=

1

20

mv2
k=

mv2

10×x2

Substituting the values in the above equation, we get
k=

40000×(72× 5 18 )2

10(1)2

= 16 × 105 N / m
Comparing the spring constant, k = x × 105
The value of the x = 16.