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  • If velocity [V] time [T] and force [F] are chosen as the base quantities, the dimensions of the mass will be :  Option: 1 <img alt="\left[\mathrm{FVT}^{-1}\right]" src="https://entrancecorner.codecogs.com/gif.latex?%5Cleft%5B%5Cmat

If velocity [V] time [T] and force [F] are chosen as the base quantities, the dimensions of the mass will be :
 
Option: 1 \left[\mathrm{FVT}^{-1}\right]
Option: 2 \left[\mathrm{FTV}^{-1}\right]
Option: 3 \left[\mathrm{FT}^{2} \mathrm{~V}\right]
Option: 4 \left[\mathrm{FT}^{-1} \mathrm{~V}^{-1}\right]

Answers (1)

best_answer

Mass\: \alpha \: F^{x}V^{y}T^{z}\\

\left [ M^{1} \right ]=\left [ M^{1}L^{1}T^{-2} \right ]^{x}\left [ L^{1}T^{-1} \right ]^{y}\left [ T \right ]^{z}\\

\left [ M^{1}L^{0}T^{0} \right ]=\left [ M^{x}L^{x+y}T^{-2x-y+z} \right ]

Comparing both sides

x=1\\  ...........(1)

x+y=0\\

y=-1\\     .............(2)

-2x-y+z=0\\-2-(-1)+z=0\\

z=1\\   ...........(3)

\left [ Mass \right ]=\left [ F^{1}V^{-1}T^{1} \right ]

The correct option is (2)

 

Posted by

vishal kumar

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