Question

If velocity p, acceleration q and density r are taken
as fundamental quantities, then the dimensional
formula for kinetic energy kis
(1) 08 2013
(2) p2r8q3
(3) p?rge
(4) perg3​

Answer 1

Answer:

$\bf K.E.=kp^8q^{-3}r^1$

Step-by-step explanation:

$We \ have \ to \ find \ dimensional \ formula \ for \ kinetic \ energy\\taking \ velocity \ p, \ acceleration \ q \ and \ density \ r \ are \ taken \ as \ fundamental \ quantities.\\\\K.E. =kp^aq^br^c \ ...(i)\\\\we \ know \ dimensional \ formula \ of \ energy=\left [ML^2T^{-2}\right]\\ \\ velocity=\left [LT^{-1}\right] \\\\acceleration=\left [LT^{-2}\right] \\\\density=\left [ML^{-3}}\right]\\\\ putting \ values \ here$ $\left [ML^2T^{-2}\right] =\left [LT^{-1}\right]^a\left [LT^{-2}\right]^b\left [ML^{-3}]^c\right\\\\\\\left[ML^2T^{-2}\right] =\left[ M\right]^c\left[ L\right]^{a+b-3c}\left[ T\right]^{-a-2b}\\\\From \ this \ get \ have\\\\c=1\\\\a=2-2b\\\\a=5-b\\\\we \ get\\\\b=-3 \ and \ a=8\\\\putting \ in \ equation \ (i)\\\\K.E.=kp^aq^br^c\\\\K.E.=kp^8q^{-3}r^1\\\\Thus \ we \ get \ our \ answer.$