Question:
The resistance of 2 km of a subway track with cross-sectional area 20 $cm^2$ is (in ohm) as a multiple of the specific resistance of steel $\rho$: ________.
The resistance of 2 km of a subway track with cross-sectional area 20 $cm^2$ is (in ohm) as a multiple of the specific resistance of steel $\rho$: ________.
Show Hint
Always convert all values to SI units (meters and $m^2$) before calculating.
Updated On: Jun 26, 2026
- $10^{2} \rho$
- $10^{3} \rho$
- $10^{4} \rho$
- $10^{5} \rho$
- $10^{6} \rho$
Show Solution
Verified By Collegedunia
The Correct Option is
Solution and Explanation
Step 1: Concept
Resistance $R = \rho (L/A)$.
Step 2: Meaning
Convert units to meters: $L = 2 \text{ km} = 2 \times 10^{3} \text{ m}$; $A = 20 \text{ cm}^2 = 20 \times 10^{-4} \text{ m}^2 = 2 \times 10^{-3} \text{ m}^2$.
Step 3: Analysis
$R = \rho \times (2 \times 10^{3} / 2 \times 10^{-3})$.
Step 4: Conclusion
$R = \rho \times 10^{6} = 10^{6} \rho$. Final Answer: (E)
Resistance $R = \rho (L/A)$.
Step 2: Meaning
Convert units to meters: $L = 2 \text{ km} = 2 \times 10^{3} \text{ m}$; $A = 20 \text{ cm}^2 = 20 \times 10^{-4} \text{ m}^2 = 2 \times 10^{-3} \text{ m}^2$.
Step 3: Analysis
$R = \rho \times (2 \times 10^{3} / 2 \times 10^{-3})$.
Step 4: Conclusion
$R = \rho \times 10^{6} = 10^{6} \rho$. Final Answer: (E)
Was this answer helpful?
0
0
Top KEAM Physics Questions
- A body oscillates with SHM according to the equation (in SI units), $x = 5 cos \left(2\pi t +\frac{\pi}{4}\right) .$ Its instantaneous displacement at $t = 1$ second is
Kepler's second law (law of areas) of planetary motion leads to law of conservation of
- Two capillary tubes A and B of diameter $1\, mm$ and $2\, mm$ respectively are dipped vertically in a liquid. If the capillary rise in A is 6 cm, then the capillary rise in B is
- In the circuit given in figure, 1 and 2 are ammeters. Just after key K is pressed to complete the circuit, the reading will be
- A plate has a length $ 5\pm 0.1\text{ }cm $ and breadth $ 2\pm 0.01\text{ }cm $ . Then the area of the plate is:
View More Questions
Top KEAM Resistance Questions
- Two wires of the same material having equal area of cross section have lengths L and 2L. Their respective resistances are in the ratio
- A uniform wire of resistance 9 $\Omega$ is joined end-to-end to form a circle. Then the resistance of the circular wire between any two diametrically opposite points is
- The resistance of a wire at room temperature $ 30{}^\circ C $ is found to be $ 10\,\Omega $ . Now to increase the resistance by 10%, the temperature of the wire must be [The temperature coefficient of resistance of the material of the wire is $ 0.002/{}^\circ C $ ]
- A metallic cylindrical wire 'A' has length 10 cm and radius 3 mm. Another hollow cylindrical wire 'B' of the same metal has length 10 cm, inner radius 3 mm and outer radius 4 mm. The ratio of the resistance of the wires A to B is:
- Find the effective resistance between points A and B. Each resistance is equal to R.
View More Questions
Top KEAM Questions
- i.$\quad$ They help in respiration ii.$\quad$ They help in cell wall formation iii.$\quad$ They help in DNA replication iv. $\quad$They increase surface area of plasma membrane Which of the following prokaryotic structures has all the above roles?
- A body oscillates with SHM according to the equation (in SI units), $x = 5 cos \left(2\pi t +\frac{\pi}{4}\right) .$ Its instantaneous displacement at $t = 1$ second is
- The pH of a solution obtained by mixing 60 mL of 0.1 M BaOH solution at 40m of 0.15m HCI solution is
Kepler's second law (law of areas) of planetary motion leads to law of conservation of
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
View More Questions