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JEE Main 2014 (19 Apr, Shift 1) · Gravitational Potential & Energy

Gravitational Potential & Energy question from JEE Main 2014 (19 Apr, Shift 1)

Q28JEE Main 2014 · 19 APR · SHIFT 1Medium

Gravitational Potential & Energy

The gravitational field in a region is given byg⃗=\vec{g} = 5 N/kg i^5\text{ N/kg}\,\hat{i} ++ 12 N/kg j^12\text{ N/kg}\,\hat{j}. The change in the gravitational potential energy of a particle of mass 1 kg when it is taken from the origin to a point (7m, −- 3m) is:

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Answer: (d)

  1. ΔU=−m∫g⃗⋅dr⃗=−m(gxΔx+gyΔy)\Delta U = -m\int \vec{g}\cdot d\vec{r} = -m(g_x\Delta x + g_y\Delta y)
  2. ΔU=−1 (5×7+12×(−3))=−(35−36)\Delta U = -1\,(5\times7 + 12\times(-3)) = -(35 - 36)
  3. ΔU=1 J\Delta U = 1\ \text{J}
  4. So the answer is (d) 1 J.
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