Gravitation

JEE Main level, single correct, medium

151 of 223

Question 151 of 223

The gravitational field in a region is given by g⃗=(5i^+12j^)Nkg−1\vec{g}=\left(5\hat{\text{i}}+12\hat{j}\right)N{kg}^{-1}. The change in the gravitational potential energy of a particle of mass 2kg2kg when it is taken from the origin to a point (7m,−3m)\left(7m,-3m\right) is

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Answer: (C) 2J2 \text{J}

dV=−g⃗.dr⃗dV=-\vec{g}.\vec{dr}
⇒∆V=−g⃗.∆r⃗\Rightarrow ∆V=-\vec{g}.∆\vec{r}
=−(5i^+12j^)⋅(7i^−3j^)=-\left(5\hat{\text{i}}+12\hat{\text{j}}\right)\cdot \left(7\hat{\text{i}}-3\hat{\text{j}}\right)
=−(35−36)=1=-\left(35-36\right)=1

⇒ΔU=mΔV=2J\text{⇒Δ}\text{U}=\text{m}\text{Δ}\text{V}=2J

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