Respected Sir/Mam
This question is not from above mentioned topics , it is from previous year.
Q. A particle moves in x-y plane under the influence of a force such that its linear momentum is p(t)=[i  cos (alphat)- j sin (alpha t)] beta , where alpha and beta are constants. What is the angle between force and momentum?

Asked by Kb Aulakh | 27th Apr, 2015, 11:20: PM

Expert Answer:

begin mathsize 12px style straight F with rightwards arrow on top space equals space fraction numerator straight d straight p with rightwards arrow on top over denominator dt end fraction space straight F with rightwards arrow on top space equals space straight d over dt space open square brackets straight i space cos space αt space minus space straight j space sin space αt close square brackets space straight beta straight F with rightwards arrow on top space equals space αβ space open square brackets negative straight i space sin space αt minus space straight j space cos space αt space close square brackets space Now comma space straight F with rightwards arrow on top space times space straight P with rightwards arrow on top space equals space open vertical bar straight F with rightwards arrow on top close vertical bar open vertical bar straight p with rightwards arrow on top close vertical bar cos space straight theta cos space straight theta space equals space fraction numerator straight F with rightwards arrow on top space times space straight P with rightwards arrow on top over denominator open vertical bar straight F with rightwards arrow on top close vertical bar open vertical bar straight p with rightwards arrow on top close vertical bar end fraction open vertical bar straight F with rightwards arrow on top close vertical bar space equals αβ space square root of left parenthesis negative sin space αt right parenthesis squared space plus left parenthesis cos space αt right parenthesis squared space space end root space equals space plus-or-minus space αβ open vertical bar straight p with rightwards arrow on top close vertical bar space equals straight beta space square root of left parenthesis cos space αt right parenthesis squared space plus left parenthesis negative sin space αt right parenthesis squared space space end root space equals space plus-or-minus space straight beta straight F with rightwards arrow on top space times space straight P with rightwards arrow on top space equals space minus space cosαt space times space sin space αt space plus space sin space αt space times space cos space αt space equals space 0 hence comma cos space straight theta space equals space fraction numerator 0 over denominator αβ space cross times space straight beta end fraction space equals space 0 space therefore space straight theta space equals space 90 to the power of ring operator end style
 
Hence,  the angle between force and momentum is 90º

Answered by Priyanka Kumbhar | 28th Apr, 2015, 10:57: AM