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Work, Energy And Power

Question
CBSEENPH11017248

A body moves under a force such that momentum of body at any instant is,

straight p with rightwards arrow on top space equals space straight p space cost space straight i with hat on top space plus space straight p space sint space straight j with hat on top 

What is the rate of work done by the force?

Solution
Since the momentum of the body at any instant is given by,
             straight p with rightwards arrow on top space equals space straight p space cost space straight i with hat on top space plus space straight p space sint space straight j with hat on top 
∴ Force is given by, straight F with rightwards arrow on top equals fraction numerator straight d straight p with rightwards arrow on top over denominator dt end fraction equals negative straight p space sint space straight i with hat on top plus straight p space cost space straight i with hat on top 
We know, the rate of work done is power P which is given by, 
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  equals fraction numerator left parenthesis negative straight p space sint space straight i with hat on top plus straight p space cost space straight j with hat on top right parenthesis times left parenthesis straight p space cost space straight i with hat on top plus straight p space sint space straight j with hat on top right parenthesis over denominator straight m end fraction 
  equals fraction numerator negative straight p squared sint space cost space plus space straight p squared space cost space sint over denominator straight m end fraction equals 0 
∴  Rate of work done is zero.