A physical quantity has term of velocity,and force which are proportional to it .It is known that it does not depend on any other physical quantity ,so its dimension can be,
$M L^{2} T^{- 3}$
$M L^{2} T^{3}$
$M L T^{3}$
none of the above

Question

A physical quantity has term of velocity,and force which are proportional to it .It is known that it does not depend on any other physical quantity ,so its dimension can be,
$M L^{2} T^{- 3}$
$M L^{2} T^{3}$
$M L T^{3}$
none of the above

Toppr Admin · Accepted Answer

Let- x be the physical quantity-Here- x-x221D-v a-xA0-x-x221D-F where v- velocity and F- forcex-kvF where k- proportionality constant- -xA0-Dimensionally- -xA0-x-LT-x2212-1-MLT-x2212-2-ML2T-x2212-3-

A physical quantity has term of velocity,and force which are proportional to it .It is known that it does not depend on any other physical quantity ,so its dimension can be,ML2T−3ML2T3MLT3none of the above

Let, x be the physical quantity.Here, x∝v ax∝F where v= velocity and F= forcex=kvF where k= proportionality constant. Dimensionally, [x]=[LT−1][MLT−2]=[ML2T−3]

A physical quantity has term of velocity,and force which are proportional to it .It is known that it does not depend on any other physical quantity ,so its dimension can be,
$M L^{2} T^{- 3}$
$M L^{2} T^{3}$
$M L T^{3}$
none of the above

Let, $x$ be the physical quantity.
Here, $x \propto v$ a $x \propto F$ where $v =$ velocity and $F =$ force
$x = k v F$ where $k =$ proportionality constant.
Dimensionally, $[x] = [L T^{- 1}] [M L T^{- 2}] = [M L^{2} T^{- 3}]$