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

(B) The gravitational field is given by $E = (5\hat{i} + 12\hat{j}) \,N/kg$. The displacement vector $dr$ from the origin $(0, 0)$ to the point $(12 \

Vedclass · Accepted Answer

$-240$

Vedclass · Answer

(B) The gravitational field is given by $E = (5\hat{i} + 12\hat{j}) \,N/kg$. The displacement vector $dr$ from the origin $(0, 0)$ to the point $(12 \,m, 5 \,m)$ is $dr = (12\hat{i} + 5\hat{j}) \,m$. The change in gravitational potential $dV$ is given by $dV = -E \cdot dr$. $dV = -(5\hat{i} + 12\hat{j}) \cdot (12\hat{i} + 5\hat{j}) = -(5 	imes 12 + 12 	imes 5) = -(60 + 60) = -120 \,J/kg$. The change in gravitational potential energy $\Delta U$ is given by $\Delta U = m \cdot dV$. Given mass $m = 2 \,kg$, we have $\Delta U = 2 \,kg 	imes (-120 \,J/kg) = -240 \,J$.

The gravitational field in a region is given by the equation $E = (5\hat{i} + 12\hat{j}) \,N/kg$. If a particle of mass $2 \,kg$ is moved from the origin to the point $(12 \,m, 5 \,m)$ in this region, what is the change in gravitational potential energy (in $\,J$)?

Similar Questions

If $W_1, W_2$ and $W_3$ represent the work done in moving a particle from $A$ to $B$ along three different paths $1, 2$ and $3$ (as shown in the figure) in the gravitational field of the point mass '$m$',find the correct relation between '$W_1$','$W_2$' and '$W_3$'.

Write $SI$ and $CGS$ unit of gravitational potential.

Two bodies of masses $m$ and $M$ are placed at a distance $d$ from each other. What is the gravitational potential $V$ at the point where the gravitational field intensity is zero?

The self gravitational potential energy of a spherical shell of mass $M$ and radius $R$ is

If the gravitational field intensity at a point is given by $E = K/x^3$,what is the gravitational potential at that point?

Vedclass Test Series

Exam Paper Generator

Online Exam Module