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Work Power and Energy question

2022 · 29 Jun · Shift 2 · Q57
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Work Power and Energy question

2022 · 29 Jun · Shift 2 · Q57

JEE MainPhysicsWork Power and EnergyMCQ+4 / −1
In the given figure, the block of mass m is dropped from the point 'A'. The expression for kinetic energy of block when it reaches point 'B' is JEE Main 2022 (Online) 29th June Evening Shift Physics - Work Power & Energy Question 70 English
  1. A
    12mg y02{1 \over 2}mg\,{y_0}^221​mgy0​2
  2. B
    12mg y2{1 \over 2}mg\,{y^2}21​mgy2
  3. C
    mg(y−y0)mg(y - {y_0})mg(y−y0​)
  4. D
    mgy0mg{y_0}mgy0​
View written solutionFree

Correct answer: D

  1. Use conservation of mechanical energy

The block is dropped from rest at point AAA, so initially KA=0.K_A = 0.KA​=0.

If the block falls vertically downward by a height y0y_0y0​ to reach point BBB, then the loss in gravitational potential energy is

DeltaU=mgy0. Delta U = mg y_0.DeltaU=mgy0​.

Since no non-conservative work is mentioned, this loss in potential energy becomes the gain in kinetic energy: KB=mgy0.K_B = mg y_0.KB​=mgy0​.

  1. Check dimensions of the options

Kinetic energy must have dimensions of energy.

  • Option A: 12mgy02\frac12 mg y_0^221​mgy02​ has dimensions [force]×[length]2[force]\times[length]^2[force]×[length]2, not energy.
  • Option B: 12mgy2\frac12 mg y^221​mgy2 also has wrong dimensions.
  • Option C: mg(y−y0)mg(y-y_0)mg(y−y0​) depends on another variable and is not the correct drop from AAA to BBB here.
  • Option D: mgy0mg y_0mgy0​ has correct dimensions and matches energy conservation.
  1. Conclusion

Therefore, the kinetic energy of the block at point BBB is mgy0.\boxed{mg y_0}. mgy0​​.

So the correct option is D.

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