To find the distance $d$ over which a signal can be seen clearly in foggy conditions, a railways engineer uses dimensional analysis and assumes that the distance depends on the mass density $\rho$ of the fog, intensity (power/area) $S$ of the light from the signal and its frequency $f$. The engineer find that $d$ is proportional to $S ^{1 / n}$. The value of $n$ is:
IIT 2014, Advanced
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1In an experiment to find out the diameter of wire using screw gauge, the following observation were noted.View Solution
$(a)$ Screw moves $0.5\,mm$ on main scale in one complete rotation
$(b)$ Total divisions on circular scale $=50$
$(c)$ Main scale reading is $2.5\,mm$
$(d)$ $45^{\text {th }}$ division of circular scale is in the pitch line
$(e)$ Instrument has $0.03 \;mm$ negative error
Then the diameter of wire is $...........\,mm$
- 2View SolutionThe dimension of Planck constant equals to that of
- 3A system has basic dimensions as density $[D]$, velocity $[V]$ and area $[A]$. The dimensional representation of force in this system isView Solution
- 4View SolutionThe nuclear cross-section is measured in barn, it is equal to
- 5The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are $1 \%, 2 \%$ and $3 \%$ respectively. The maximum percentage error in the detection of the dissipated heat will beView Solution
- 6A student measured the length of a rod and wrote it as $3.50\;cm$. Which instrument did he use to measure it?View Solution
- 7The length, breadth and thickness of a block are given by $l = 12\,cm,\,b = 6\,cm$ and $t = 2.45\,cm$ The volume of the block according to the idea of significant figures should beView Solution
- 8If $C$ and $V$ represent capacity and voltage respectively then what are the dimensions of $\lambda,$ where $\frac{ C }{ V }=\lambda ?$View Solution
- 9A force $F$ is given by $F = at + b{t^2}$, where $t$ is time. What are the dimensions of $a$ and $b$View Solution
- 10The dimensions of resistivity in terms of $M,\,L,\,T$ and $Q$ where $Q$ stands for the dimensions of charge, isView Solution