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Question
The gravitational field in a region is given by \[E = \left( 2 \overrightarrow{i} + 3 \overrightarrow{j} \right) N {kg}^{- 1}\] . Show that no work is done by the gravitational field when a particle is moved on the line 3y + 2x = 5.
[Hint : If a line y = mx + c makes angle θ with the X-axis, m = tan θ.]
Solution
The gravitational field in a region is given by \[\overrightarrow{E} = 2 \hat i + 3 \hat j\]
Slope of the electric field, \[m_1 = \tan \theta_1 = \frac{3}{2}\]
The given line is 3y + 2x = 5.
Slope of the line, \[m_2 = \tan \theta_2 = - \frac{2}{3}\]
We can see that m1m2 = −1
Since the directions of the field and the displacement are perpendicular to earth other, no work is done by the gravitational field when a particle is moved on the given line.
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