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  4. In a particular system, the unit of length, mass and time are chosen to be 10 mathrm~cm, 10 mathrm~g and 0.1 sec respectively. The unit of force in this system will be equivalent to:

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Q. In a particular system, the unit of length, mass and time are chosen to be $10 \mathrm{~cm}, 10 \mathrm{~g}$ and 0.1 sec respectively. The unit of force in this system will be equivalent to:

Physical World, Units and Measurements

Solution:

$\begin{aligned} \mathrm{F} &=\left(\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-2}\right) \\ &=\left[(10 \mathrm{~g})^{1}(10 \mathrm{~cm})^{1}(0.1 \mathrm{~s})^{-2}\right] \\ &=\left[\left(10^{-2} \mathrm{~kg}\right)^{1}\left(10^{-1} \mathrm{~m}\right)^{1}\left(10^{2} \mathrm{~s}^{-2}\right)\right] \\ \mathrm{F} &=10^{-1} \mathrm{~N}=0.1 \mathrm{~N} \end{aligned}$