AP EAMCET · PHYSICS · Gravitation
The gravitational field in a region is given by equation \(\mathbf{E}=(5 \mathbf{i}+12 \mathbf{j}) \mathrm{N} / \mathrm{kg}\). If a particle of mass \(2 \mathrm{~kg}\) is moved from the origin to the point \((12 \mathrm{~m}, 5 \mathrm{~m})\) in this region, the change in gravitational potential energy is
- A \(-225 \mathrm{~J}\)
- B \(-240 \mathrm{~J}\)
- C \(-245 \mathrm{~J}\)
- D \(-250 \mathrm{~J}\)
Answer & Solution
Correct Answer
(B) \(-240 \mathrm{~J}\)
Step-by-step Solution
Detailed explanation
We have, \(\begin{aligned} d V & =-E \cdot d r=-(5 \mathbf{i}+12 \mathbf{j}) \cdot(12 \mathbf{i}+15 \mathbf{j}) \\ & =(60+60)=-120\end{aligned}\) The change in gravitational potential energy \(U=m d V=2 \times(-120)=-240 \mathrm{~J}\)
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