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  • The gravitational field in a region is given by <img alt="\mathrm{\overrightarrow{\mathrm{I}}=(4 \hat{\imath}+\hat{\jmath}) \mathrm{N} / \mathrm{kg}.}" src="https://entrancecorner.oncodecogs.com/gi

The gravitational field in a region is given by \mathrm{\overrightarrow{\mathrm{I}}=(4 \hat{\imath}+\hat{\jmath}) \mathrm{N} / \mathrm{kg}.}Work done by this field is zero when the particle is moved along the line

 

Option: 1

\mathrm{y+4 x=2}
 


Option: 2

\mathrm{4 y+x=6}
 


Option: 3

\mathrm{x+y=5}
 


Option: 4

all of the above


Answers (1)

best_answer

Work done will be zero when displacement is perpendicular to the filed. The field makes an angle

\mathrm{ \theta_1=\tan ^{-1}\left(\frac{1}{4}\right) \text { with positive } x \text {-axis } }

While the line \mathrm{ y+4 x=2 } makes an angle

\mathrm{ \theta_2=\tan ^{-1}(-4) \text { with positive } x \text {-axis } }

\mathrm{ \theta_1+\theta_2=90^{\circ} \text { i.e. the line } y+4 x=2 }

is perpendicular to \mathrm{ \overline{\mathrm{I}} }.

Hence option 1 is correct.

Posted by

Rishi

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