Passage

In a certain system of absolute units the acceleration produced by gravity in a body falling freely is denoted by $$3$$, the kinetic energy of a $$272.1\:kg$$ shot moving with velocity $$448$$ meters per second is denoted by $$100$$, and its momentum by $$10$$.
Physics

The unit of length is


SOLUTION

Let unit of length, time and mass be $$L_1,T_1$$ and $$M_1$$ respectively.

According to question

$$9.8\;LT^{-2}=3\;L_1T^{-2}$$

$$\displaystyle\frac{1}{2}(272.1)(448)^2ML^2T^{-2}=100\;M_1L_1^2T_1^{-2}$$

$$(272.1)(448)\;MLT^{-1}=10M_1L_1T_1$$

by solving above equation $$L_1=153.6\:L$$

$$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=153.6\,m$$

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