In the CGS system,the magnitude of the force | vedclass

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(C) The formula for unit conversion is $n_2 = n_1 \left[ \left( \frac{M_1}{M_2} \right)^a \left( \frac{L_1}{L_2} \right)^b \left( \frac{T_1}{T_2} \rig

Vedclass · Accepted Answer

$3.6$

Vedclass · Answer

(C) The formula for unit conversion is $n_2 = n_1 \left[ \left( \frac{M_1}{M_2} ight)^a \left( \frac{L_1}{L_2} ight)^b \left( \frac{T_1}{T_2} ight)^c ight]$.Dimensions of force are $[M L T^{-2}]$,so $a=1, b=1, c=-2$.Given $n_1 = 100$,$M_1 = 1 	ext{ g}$,$L_1 = 1 	ext{ cm}$,$T_1 = 1 	ext{ s}$.New system: $M_2 = 1 	ext{ kg} = 1000 	ext{ g}$,$L_2 = 1 	ext{ m} = 100 	ext{ cm}$,$T_2 = 1 	ext{ min} = 60 	ext{ s}$.Substituting these values:$n_2 = 100 \left[ \left( \frac{1 	ext{ g}}{1000 	ext{ g}} ight)^1 \left( \frac{1 	ext{ cm}}{100 	ext{ cm}} ight)^1 \left( \frac{1 	ext{ s}}{60 	ext{ s}} ight)^{-2} ight]$$n_2 = 100 \left[ \frac{1}{1000} 	imes \frac{1}{100} 	imes (60)^2 ight]$$n_2 = 100 	imes \frac{1}{1000} 	imes \frac{1}{100} 	imes 3600$$n_2 = 3.6$.

In the $CGS$ system,the magnitude of the force is $100 \text{ dynes}$. In another system where the fundamental physical quantities are kilogram,meter,and minute,the magnitude of the force is:

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