A force F = (0.Sx +10) N acts on a particle. Calculate the work done by the force in displacing particle from x=0 to x=2 m.
Correct answer: B. 21 J
- A. 20 J
- B. 21 J
- C. 22 J
- D. 23 J
Explanation
Explanation is given below.Small amount of work done dW in giving a small displacement dx is given by dW=x or dW=Fdxcos0∘ or dW=Fdx[∴cos0∘=1] Total work done, W = ∫x=0x=2 Fdx=∫x=0x=2 (0.5x+10)dx =∫x=0x=2 0.5xdx+∫x=0x=2 10dx=0.5∣∣∣∣∣ 2x2 ∣∣∣∣∣ x=0x=2 +10∣x∣x=0x=2 =20.5 [22−02]+10(2−0]=(1+20)=21J Option A,C and D are incorrect
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About Work
Work is done when a force produces displacement, with its value determined by the component of force along the displacement. The topic covers positive, negative and zero work, work by variable forces from force-displacement graphs, and the connection between net work and change in kinetic energy.
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