#### 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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Subjective Medium Published on 18th 08, 2020
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