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  • The gravitational field in a region is given by :  <img alt="\vec{E}=\left ( 5N/kg \right )\hat{i}+\left ( 12N/kg \right )\hat{j}" src="https://learn.careers360.com/latex-image/?%5Cv

The gravitational field in a region is given by : 

\vec{E}=\left ( 5N/kg \right )\hat{i}+\left ( 12N/kg \right )\hat{j}

If the potential at the origin is taken to be zero, then the ratio of the potential at the points \left ( 12m,0 \right ) and \left ( 0,5m \right ) is : 

Option: 1

Zero
 


Option: 2

1


Option: 3

\frac{144}{25}


Option: 4

\frac{25}{144}


Answers (1)

best_answer

 

 

 

 

Gravitational field in a region is given by

\vec{E}=\left ( 5N/kg \right )\hat{i}+\left ( 12N/kg \right )\hat{j}

(Potential at origin is O)→ given

and \ we \ know \ that \ \ E=\frac{d v}{d r} \Rightarrow (d v=E d r)

In vector form, the position vector are written as

\begin{aligned} & \vec{r_1}=12 i+o j\\ & \vec{r_2}=0 \hat{i}+5 \hat{j} \end{aligned}

\begin{aligned} &d V_{1}=E \cdot d r_{1}\\ &=(5 \hat{i}+12 \hat{j}) \cdot (12 \hat{i}+0 \hat{j})=12 \times 5\\ &\begin{array}{l} d V_{2}=E \cdot d r_{2} \\ =(5 \hat{i}+12 \hat{j}) \cdot(0 \hat{i}+5 \hat{j})=5 \times 12 \\ \\ \frac{d V_{1}}{d V_{2}}=1 \end{array} \end{aligned}

Posted by

seema garhwal

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