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Given instant position r=Acoswti +Asinwtj Show that the force is conservative one.

Given instant position r=Acoswti +Asinwtj
Show that the force is conservative one.

Grade:9

1 Answers

Yuvraj Singh
askIITians Faculty 68 Points
2 years ago
Position vector r=(acoswt)i^+(asinwt)j^​Thus velocity vector v=dtdr​=(−awsinwt)i^+(awcoswt)j^​
Calculating v.r=[(−awsinwt)i^+(awcoswt)j^​].[(acoswt)i^+(asinwt)j^​]
∴v.r=−aw2sinwtcoswt+aw2sinwtcoswt=0
Hence velocity vector is perpendicular to the position vector.

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