The gravitational field in a region is given | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given, gravitational field intensity, $I = (5 \hat{i} + 12 \hat{j}) 	ext{ N kg}^{-1}$.Mass of the object, $m = 3 	ext{ kg}$.The change in gravit

Vedclass · Accepted Answer

$48$

Vedclass · Answer

(C) Given, gravitational field intensity, $I = (5 \hat{i} + 12 \hat{j}) 	ext{ N kg}^{-1}$.Mass of the object, $m = 3 	ext{ kg}$.The change in gravitational potential energy $\Delta U$ is given by the negative of the work done by the gravitational field, or $\Delta U = -W = -m \int \vec{I} \cdot d\vec{r}$.However, in many contexts, the magnitude of the change in potential energy is calculated as $\Delta U = m \int_{A}^{B} \vec{I} \cdot d\vec{r}$ considering the work done against the field.Using the formula $\Delta U = m \int_{(0,0)}^{(8,-2)} \vec{I} \cdot d\vec{r}$:$\Delta U = 3 \int_{(0,0)}^{(8,-2)} (5 \hat{i} + 12 \hat{j}) \cdot (dx \hat{i} + dy \hat{j})$$\Delta U = 3 [5x + 12y]_{(0,0)}^{(8,-2)}$$\Delta U = 3 [5(8) + 12(-2)] - 3 [5(0) + 12(0)]$$\Delta U = 3 [40 - 24] = 3 [16] = 48 	ext{ J}$.

The gravitational field in a region is given by $I = (5 \hat{i} + 12 \hat{j}) \text{ N kg}^{-1}$. The change in the gravitational potential energy of an object of mass $3 \text{ kg}$ when it is taken from the origin to a point $(8 \text{ m}, -2 \text{ m})$ is (in $\text{ J}$)

Similar Questions

Gravitational potential in a region is given by $V = -(x + y + z) \text{ J/kg}$. Find the gravitational intensity at $(2, 2, 2)$ in $\text{N/kg}$.

What is the gravitational field intensity at any point inside a uniform spherical shell?

If the distance between the centres of Earth and Moon is $D$ and the mass of Earth is $81$ times that of the Moon,at what distance from the centre of Earth will the gravitational field be zero?

$3$ particles each of mass $m$ are kept at the vertices of an equilateral triangle of side $L$. The gravitational field at the centre due to these particles is

Consider two solid spheres of radii $R_{1} = 1 \; m$ and $R_{2} = 2 \; m$ and masses $M_{1}$ and $M_{2}$,respectively. The gravitational field due to sphere $(1)$ and $(2)$ are shown in the graph. The value of $\frac{M_{1}}{M_{2}}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module