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  4. The dimension of impulse is [M2 b L3 a T4 c] . Find the value of 3a+2b-4c

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Q. The dimension of impulse is $\left[M^{2 b} L^{3 a} T^{4 c}\right]$ . Find the value of $3a+2b-4c$

NTA AbhyasNTA Abhyas 2022

Solution:

Impulse,
$J=F\times t$
$\therefore \left[\right.J\left]\right.=\left[M^{1} L^{1} T^{- 2}\right]\times \left[T^{1}\right]=\left[M^{1} L^{1} T^{- 1}\right]$
$i\cdot e\cdot ,\left[M^{2 b} L^{3 a} T^{4 c}\right]=\left[M^{1} L^{1} T^{- 1}\right]$
$\therefore 2b=1,3a=1,4c=-1$
$2b+3a-4c=1+1-\left(\right.-1\left.\right)=1+1+1=3$