Question

In C.G.S. system the magnitude of the force is 100 dynes. In another system where the fundamental physical quantities are kilogram, metre and minute, the magnitude of the force is

• A. 0.036
• B. 0.36
• C. 3.6
• D. 36

Answer 1

Answer: (C)

3.6

Answer 2

$n_{1} = 100$, $M_{1} = g$,$L_{1} = cm$, $T_{1} = \sec$ and $M_{2} = kg$,

$L_{2} = meter$, $T_{2} = m\text{inute}$, $x = 1$, $y = 1$, $z = - 2$

By substituting these values in the following conversion formula $n_{2} = n_{1}\left\lbrack \frac{M_{1}}{M_{2}} \right\rbrack^{x}\left\lbrack \frac{L_{1}}{L_{2}} \right\rbrack^{y}\left\lbrack \frac{T_{1}}{T_{2}} \right\rbrack^{2}$

$n_{2} = 100\left\lbrack \frac{gm}{kg} \right\rbrack^{1}\left\lbrack \frac{cm}{meter} \right\rbrack^{1}\left\lbrack \frac{\sec}{\text{minute}}\lbrack\rbrack^{- 2} \right\rbrack$

$n_{2} = 100\left\lbrack \frac{gm}{10^{3}gm} \right\rbrack^{1}\left\lbrack \frac{cm}{10^{2}cm} \right\rbrack^{1}\left\lbrack \frac{\sec}{60\sec}^{- 2} \right\rbrack = 3.6$