CBSE Class 11-science Answered

Please answer question number 5

Asked by arunavamitra50 | 22 Jun, 2018, 07:01: PM

Expert Answer

begin mathsize 12px style stack O A with rightwards arrow on top space equals space 2 space cos space 30 space i with rightwards arrow on top space plus 2 space sin space 30 space j with rightwards arrow on top space equals space space square root of 3 space i with rightwards arrow on top space plus space j with rightwards arrow on top space space............... left parenthesis 1 right parenthesis stack B C with rightwards arrow on top space equals space minus 1.5 space cos space 60 space i with rightwards arrow on top space plus 1.5 space sin space 60 space j with rightwards arrow on top space equals space space minus 3 over 4 space i with rightwards arrow on top space plus fraction numerator 3 square root of 3 over denominator 4 end fraction space j with rightwards arrow on top space............... left parenthesis 2 right parenthesis stack D E with rightwards arrow on top space equals space minus space j with rightwards arrow on top space space....................... left parenthesis 3 right parenthesis space end style

in the above equations

begin mathsize 12px style i with rightwards arrow on top space a n d space j with rightwards arrow on top space end style

are unit vectors along x and y direction of cartesian coordinate system.

Resultant vector is given by,

begin mathsize 12px style stack O A with rightwards arrow on top space plus space stack B C with rightwards arrow on top space plus space stack D E with rightwards arrow on top space equals space open parentheses square root of 3 space minus 3 over 4 close parentheses space i with rightwards arrow on top space plus space fraction numerator 3 square root of 3 over denominator 4 end fraction space j space equals space 0.9821 space i with rightwards arrow on top space plus space 1.299 space j with rightwards arrow on top end style

magnatiude of resultant =

begin mathsize 12px style square root of 0.9821 cross times 0.9821 space plus space 1.299 space cross times space 1.299 end root space equals 1.63 end style

x-component = ( √3 - 0.75) = 0.9821, y-component = 0.75×√3

angle with X-axis = tan^-1(1.299/0.9821) = 53°

Answered by Thiyagarajan K | 23 Jun, 2018, 11:30: AM

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