The gravitational field in a region is given by $E = (2 \vec{i} + 3 \vec{j}) N {kg}^{- 1}$ . 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.]

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Solution

The gravitational field in a region is given by $\vec{E} = 2 \hat{i} + 3 \hat{j}$ .
Slope of the electric field, $m_{1} = \tan θ_{1} = \frac{3}{2}$
The given line is 3y + 2x = 5.
Slope of the line, $m_{2} = \tan θ_{2} = - \frac{2}{3}$
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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The gravitational field in a region is given by E=2i→+3j→ 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.]

The gravitational field in a region is given by $E = (2 \vec{i} + 3 \vec{j}) N {kg}^{- 1}$ . 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.]