MHT CET · Physics · Units and Dimensions
If the dimensions of a physical quantity are given by \(\left[\mathrm{L}^{\mathrm{a}} \mathrm{M}^{\mathrm{b}} \mathrm{T}^{c}\right]\) then the physical
quantity is
- A velocity if \(a=-1, b=0, c=+1\)
- B force if \(a=-1, b=1, c=-2\)
- C pressure if \(a=-1, b=1, c=-2\)
- D acceleration if \(\mathrm{a}=1, \mathrm{~b}=1, \mathrm{c}=-2\)
Answer & Solution
Correct Answer
(C) pressure if \(a=-1, b=1, c=-2\)
Step-by-step Solution
Detailed explanation
A. pressure if \(a=1, b=-1, c=2\)
Dimensions of velocity \(=\left[\mathrm{M}^{0} \mathrm{~L}^{1} \mathrm{~T}^{-1}\right]\)
Here, \(a=0, b=1, c=-1\)
Dimension of acceleration \(=\left[\mathrm{M}^{0} \mathrm{~L}^{1} \mathrm{~T}^{-2}\right]\)
Dimension of force \(=\left[\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-2}\right]\)
Dimension of pressure \(=\left[\mathrm{M}^{1} \mathrm{~L}^{-1} \mathrm{~T}^{-2}\right.\)
The physical quantity is pressure.
Dimensions of velocity \(=\left[\mathrm{M}^{0} \mathrm{~L}^{1} \mathrm{~T}^{-1}\right]\)
Here, \(a=0, b=1, c=-1\)
Dimension of acceleration \(=\left[\mathrm{M}^{0} \mathrm{~L}^{1} \mathrm{~T}^{-2}\right]\)
Dimension of force \(=\left[\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-2}\right]\)
Dimension of pressure \(=\left[\mathrm{M}^{1} \mathrm{~L}^{-1} \mathrm{~T}^{-2}\right.\)
The physical quantity is pressure.
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