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JEE Main 2022 · 26 Jun · Shift 2, Physics question 33

Arrange the four graphs in descending order of total work done; where W1W_1, W2W_2, W3W_3 and W4W_4 are the work done corresponding to figure a, b, c and d respectively.

Four force-displacement graphs. (a) F rises linearly from −F at x = 0, through zero at x0, to +F at x1. (b) F rises linearly from −F, through zero at x0, to +F at x1, then stays at F to x2. (c) F rises from −F, through zero at x0, to F at x1, stays at F to x2, then falls linearly to zero. (d) F falls linearly from +F at x = 0, through zero at x0, to −F at x1, stays at −F to x2, then jumps up to a positive spike at x3.
Choose one option
Answer and worked solution

Official answer: A

Work = signed area under F-x.

  • (a): negative triangle then an equal positive triangle: about zero.
  • (b): the same, plus a positive rectangle.
  • (c): as (b), plus a further positive triangle: largest.
  • (d): small positive triangle, then a larger negative region: negative overall.

Order. W3>W2>W1>W4W_3>W_2>W_1>W_4.

(A)

Topics:Work by constant and variable forces
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