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If an object has angular displacement of 60 radian in 4th second and 30 radian in 8th second ,then find its angular displacement in 10th second.

Asked by thakursonali2000 | 15th Oct, 2015, 02:46: PM

Expert Answer:

$begin mathsize 12px style here comma space straight theta subscript 4 th end subscript space equals space 60 space rad space and space straight theta subscript 8 th end subscript space equals space 30 space rad Now space displacment space covered space by space the space body space in space nth space second space of space its space motion space is space gien space by comma straight S subscript nt equals straight w subscript 0 plus straight alpha over 2 left parenthesis 2 straight n minus 1 right parenthesis Since comma space straight theta subscript 4 th end subscript space equals space 60 space and space straight n space equals space 4 60 space equals space straight w subscript 0 plus straight alpha over 2 left parenthesis 2 cross times 4 minus 1 right parenthesis 60 equals straight w subscript 0 plus 7 over 2 straight alpha space space space space space space left parenthesis straight i right parenthesis straight theta subscript 8 th end subscript space equals space 30 space rad space and space straight n space equals space 8 30 space equals space straight w subscript 0 plus straight alpha over 2 left parenthesis 2 cross times 8 minus 1 right parenthesis 30 equals straight w subscript 0 plus 15 over 2 straight alpha space space space space space space left parenthesis ii right parenthesis substracting space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis straight alpha space equals space minus fraction numerator 7.5 over denominator 2 end fraction rad divided by straight s squared substituting space in space left parenthesis straight i right parenthesis 60 equals straight w subscript 0 plus 7 over 2 cross times fraction numerator negative 7.5 over denominator 2 end fraction straight w subscript 0 equals 60 plus 13.125 equals 73.125 space rad divided by straight s displacement space in space 10 th space sec straight theta space equals space 73.125 minus fraction numerator 7.5 over denominator 2 end fraction left parenthesis 2 cross times 10 minus 1 right parenthesis straight theta equals 73.125 minus 71.25 equals 1.875 space rad end style$

Answered by Priyanka Kumbhar | 16th Oct, 2015, 05:25: PM

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