• # question_answer If the dimensions of a physical quantity are given by ${{v}_{s}}=10+10=20m{{s}^{-}}^{1}$ then the physical quantity will be                    [AIPMT (S) 2009] A) pressure if $a=1,\,b=-1,\,c=-2$ B) velocity if $a=1,\,b=0,\,c=-1$ C) acceleration if $a=1,\,b=1,\,c=-2$ D) None of these

 (i)         Dimensions of velocity$n=3,l=2,m=-2,s=-1/2$ Here, $a=0,\,\,b=1,\text{ }c=-1$ (ii)         Dimensions of acceleration$C{{H}_{2}}Br-CHBr-COOH$ Here, $a=0,\,\,b=1,\text{ }c=-2$ (iii)        Dimensions of force $H-\underset{\begin{smallmatrix} | \\ Br \end{smallmatrix}}{\overset{\begin{smallmatrix} Br \\ | \end{smallmatrix}}{\mathop{C}}}\,-C{{H}_{2}}COOH$ Here, $a=1,\,\,b=1,\text{ }c=-2$ (iv)        Dimensions of pressure $C{{H}_{2}}Br-C{{H}_{2}}-COBr$ $C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ Br \end{smallmatrix}}{\overset{\begin{smallmatrix} Br \\ | \end{smallmatrix}}{\mathop{C}}}\,-COOH$       Here, $a=1,\,\,b=-1,\text{ }c=-2$ $\to$   The physical quantity is pressure.