AP EAMCET · PHYSICS · Work Power Energy
If a force of \(\left(6 x^2-4 x\right) \mathrm{N}\) acts on a body of mass 10 kg, then work to be done by the force in displacing the body from \(x=2 m\) to \(x=4 m\) is
- A 22 J
- B 44 J
- C 66 J
- D 88 J
Answer & Solution
Correct Answer
(D) 88 J
Step-by-step Solution
Detailed explanation
\(W = \int_{x_1}^{x_2} F(x) \, dx\) \(W = \int_{2}^{4} (6x^2 - 4x) \, dx\) \(W = \left[ 2x^3 - 2x^2 \right]_{2}^{4}\) \(W = (2(4)^3 - 2(4)^2) - (2(2)^3 - 2(2)^2)\) \(W = (128 - 32) - (16 - 8)\) \(W = 96 - 8 = 88 \mathrm{J}\)
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