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) \[force\,\,if\,\,a=0,\,\,b=-1,\,\,c=-2\]
Correct Answer: A
Solution :
(i) Dimensions of velocity \[=\,\,\left[ {{M}^{0}}{{L}^{1}}{{T}^{-1}} \right]\] Here, \[a\text{ }=0,\,\,b=1,\,\,c=-1\]. (ii) Dimensions of acceleration \[=\,\,\left[ {{M}^{0}}{{L}^{1}}{{T}^{-2}} \right]\] Here, \[a\text{ }=0,\,\,6=\text{ }1,\,\,c=-2\] (iii) Dimensions of force \[=\,\,\left[ {{M}^{1}}{{L}^{1}}{{T}^{-2}} \right]\] Here, \[\operatorname{a} =1, b=1,\,T=-2\] (iv) Dimensions of pressure \[=\,\,\left[ {{M}^{1}}{{L}^{-1}}{{T}^{-2}} \right]\] \[\therefore \,\,\,\,Here\,\,a=1,\,\,b=-1,\,\,c=-2\] \[\therefore \] The physical quantity is pressure.
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