Question 447: Gravitation

Question

The gravitational field in a region is given by $$\mathbf{E}=5 \mathrm{~N} / \mathrm{kg} \hat{\mathbf{i}}+12 \mathrm{~N} / \mathrm{kg} \hat{\mathbf{j}}$$. The change in the gravitational potential energy of a particle of mass $$1 \mathrm{~kg}$$ when it is taken from the origin to a point ($$5 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}$$) is

Accepted Answer

$$\begin{aligned}
& E=-\frac{d V}{d r} \
& V=\left(-\int_\limits0^x E_x d x-\int_\limits0^y E_y d yight)=-\left(E_x \cdot x+E_y \cdot yight) \
& V=-(5 	imes 5+12 	imes(-5))=-(25-60)=35 \mathrm{~J} / \mathrm{kg}
\end{aligned}$$
i.e., change is gravitational potential $$=35 \mathrm{~J} / \mathrm{kg}$$.
Hence, change in gravitational potential energy $$=35 \mathrm{~J}$$.

Answer

$$71 \mathrm{~J}$$

Answer

$$13 \sqrt{58} \mathrm{~J}$$

Answer

$$-71 \mathrm{~J}$$

Answer

$$35 \mathrm{~J}$$

Gravitation

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