CBSE Class 7 Answered

If density,acceleration and force are taken as base quantities, then time period has dimensions

a)one-sixth in force

b)minus one-sixth in density

c)minus two-third in acceleration

d)all are true

Asked by jhilmilsoma | 16 Aug, 2015, 04:31: PM

Expert Answer

begin mathsize 12px style density comma straight d space equals space open square brackets straight L to the power of negative 3 end exponent space straight M to the power of 1 space straight T to the power of 0 close square brackets acceleration comma straight a space equals space open square brackets straight L to the power of 1 space straight M to the power of 0 space straight T to the power of negative 2 end exponent close square brackets force comma space straight F space equals space open square brackets straight L to the power of 1 space straight M to the power of 1 space straight T to the power of negative 2 end exponent close square brackets Time comma space straight T space equals space space open square brackets straight L to the power of 0 space straight M to the power of 0 space straight T to the power of 1 close square brackets Consider space density comma acceleration space and space force space are space taken space as space the space base space quantities. Time space period space is space given space as comma open square brackets straight L to the power of 0 space straight M to the power of 0 space straight T to the power of 1 close square brackets space equals space straight d to the power of straight x space straight a to the power of straight y space straight F to the power of straight z open square brackets straight T to the power of 1 close square brackets space equals space open square brackets straight L to the power of negative 3 end exponent space straight M to the power of 1 space straight T to the power of 0 close square brackets to the power of straight x space end exponent open square brackets straight L to the power of 1 space straight M to the power of 0 space straight T to the power of negative 2 end exponent close square brackets to the power of straight y space end exponent open square brackets straight L to the power of 1 space straight M to the power of 1 space straight T to the power of negative 2 end exponent close square brackets to the power of straight y open square brackets straight T to the power of 1 close square brackets space equals space open square brackets straight L close square brackets to the power of negative 3 straight x space plus space straight y space plus space straight z end exponent space space open square brackets straight a close square brackets to the power of straight x space plus space straight z space end exponent space open square brackets straight F close square brackets to the power of negative 2 straight y space minus space 2 straight z end exponent Applying space principle space of space homogeneity space of space dimensions comma space we space get 0 space equals space minus 3 straight x space plus space straight y space plus space straight z space space space left parenthesis straight i right parenthesis 0 space equals space straight x space plus space straight z space space space space space space space space space space space space space space space space space left parenthesis ii right parenthesis 1 space equals space minus 2 straight y space minus space 2 straight z space space space space space space space space left parenthesis iii right parenthesis space Solving space equation space left parenthesis straight i right parenthesis space and space left parenthesis iii right parenthesis space we space get straight x space equals space minus 1 over 6 Substituting space value space in space eq. space left parenthesis straight i right parenthesis straight z space equals space 1 over 6 Substituting space in space eq. space left parenthesis iii right parenthesis straight y space equals space minus 2 over 3 Hence comma space Dimensions space of space time space period space are open square brackets straight T close square brackets space equals space straight d to the power of negative 1 divided by 6 end exponent space straight a to the power of negative 2 divided by 3 end exponent space straight F to the power of 1 divided by 6 end exponent Therefore comma space all space the space options space are space true. end style

Answered by Priyanka Kumbhar | 17 Aug, 2015, 09:05: AM

CBSE Class 7 Answered

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