# A train moving with a velocity of 30 km/h has a kinetic energy of 52000 J. When the velocity of train is increased to 60 km/h, the work done is:

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A train moving with a velocity of 30 km/h has a kinetic energy of 52000 J. When the velocity of train is increased to 60 km/h, the work done is:
1. Work done = 0
2. 156000 J
3. 104000 J
4. 52000 J

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Correct Answer - Option 2 : 156000 J

CONCEPT:

• Work-energy theorem: It states that the sum of work done by all the forces acting on a body is equal to the change in the kinetic energy of the body i.e.,

Work done by all the forces = Kf - Ki

$W = \frac{1}{2}m{v^2} - \frac{1}{2}m{u^2} = {\bf{Δ }}K$

Where v = final velocity, u = initial velocity and m = mass of the body

CALCULATION:

It is given that,
Initial velocity (u) = 30 km/h = (30 × 1000/3600) = 25/3 m/s

Initial Kinetic energy (KEi) = 52000 = $\frac{1}{2}mu^2$

Final Velocity (v) = 60 km/h = (60 × 1000/3600) = 50/3 m/s = 2u

Final kinetic energy (KEf) = $\frac{1}{2}mv^2 = \frac{1}{2}m (2u)^2 =4 KE_i$

KE = 4 × 52000 = 208000 J
According to the work-energy theorem,

⇒  Work done = Change in K.E
⇒  Work done (W) = Δ K.E = KEf - KEi = 208000 - 52000 = 156000 J