Search any question & find its solution
Question:
Answered & Verified by Expert
In CGS system the magnitude of the force is 100 dynes. In another system where the fundamental physical. quantities are kilogram, meter and minute, the magnitude of the force is
Options:
Solution:
2122 Upvotes
Verified Answer
The correct answer is:
$3.6$
$n_2=n_1\left[\left(\frac{m_1}{m_2}\right)^a\left(\frac{L_1}{L_2}\right)^b\left(\frac{T_1}{T_2}\right)^c\right]$
Dimensions of force is [ $\mathrm{M} \mathrm{L} \mathrm{T}^{-2}$ ]
$a=1, b=1, c=-2$
$\begin{aligned} n_2 & =100\left[\left(\frac{\mathrm{g}}{\mathrm{kg}}\right)^1\left(\frac{\mathrm{cm}}{\text { metre }}\right)^1\left(\frac{\mathrm{sec}}{\mathrm{min}}\right)^{-3}\right] \\ & =100\left[\frac{\mathrm{g}}{100 \mathrm{~g}} \times \frac{\mathrm{cm}}{100 \mathrm{~cm}} \times\left(\frac{\mathrm{sec}}{60 \mathrm{sec}}\right)^{-2}\right] \\ & =100\left[\frac{1}{1000} \times \frac{1}{100} \times(60)^2\right] \\ & =100 \times \frac{1}{1000} \times \frac{1}{100} \times 3600=3.6\end{aligned}$
Dimensions of force is [ $\mathrm{M} \mathrm{L} \mathrm{T}^{-2}$ ]
$a=1, b=1, c=-2$
$\begin{aligned} n_2 & =100\left[\left(\frac{\mathrm{g}}{\mathrm{kg}}\right)^1\left(\frac{\mathrm{cm}}{\text { metre }}\right)^1\left(\frac{\mathrm{sec}}{\mathrm{min}}\right)^{-3}\right] \\ & =100\left[\frac{\mathrm{g}}{100 \mathrm{~g}} \times \frac{\mathrm{cm}}{100 \mathrm{~cm}} \times\left(\frac{\mathrm{sec}}{60 \mathrm{sec}}\right)^{-2}\right] \\ & =100\left[\frac{1}{1000} \times \frac{1}{100} \times(60)^2\right] \\ & =100 \times \frac{1}{1000} \times \frac{1}{100} \times 3600=3.6\end{aligned}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.