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1.Units, Dimensions and Measurement
hard
If the dimensions of a physical quantity are given by $M^aL^bT^c$ ,then physical quantity will be
Avelocity if $a=1,b=0,c=-1$
Bacceleration if $a=1,b=1,c=-2$
Cforce if $a=0,b=-1,c=-2$
Dpressure if $a=1,b=-1,c=-2$
(AIPMT-2009)
Solution
Pressure, $p = \frac{{force}}{{area}} = \frac{{mass\, \times \,acceleration}}{{area}}$
$\therefore \,\left[ P \right] = \frac{{{M^1}L{T^{ – 2}}}}{{{L^2}}} = \left[ {{M^1}{L^{ – 1}}{T^{ – 2}}} \right] = \,{M^a}{L^b}{T^c}$
$\therefore \,a = 1,\,b = – 1,\,c = – 2.$
$\therefore \,\left[ P \right] = \frac{{{M^1}L{T^{ – 2}}}}{{{L^2}}} = \left[ {{M^1}{L^{ – 1}}{T^{ – 2}}} \right] = \,{M^a}{L^b}{T^c}$
$\therefore \,a = 1,\,b = – 1,\,c = – 2.$
Standard 11
Physics
