AP EAMCET · PHYSICS · Work Power Energy
If a position dependent force \(\left(3 x^2-2 x+7\right) \mathrm{N}\) acting on a body of mass 2 kg displaces it from \(x=0 \mathrm{~m}\) to \(x=5 \mathrm{~m}\), then the work done by the force is
- A 165 J
- B 115 J
- C 150 J
- D 135 J
Answer & Solution
Correct Answer
(D) 135 J
Step-by-step Solution
Detailed explanation
\(W = \int_{x_1}^{x_2} F(x) \,dx\) \(W = \int_{0}^{5} (3x^2 - 2x + 7) \,dx\) \(W = \left[ x^3 - x^2 + 7x \right]_{0}^{5}\) \(W = (5^3 - 5^2 + 7(5)) - (0^3 - 0^2 + 7(0))\) \(W = 125 - 25 + 35 = 135 \, \mathrm{J}\)
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