Question

Assertion: The electrical resistance of a column of $0.05\mathrm{M}$ NaOH solution of diameter $1\mathrm{cm}$ and length $50\mathrm{cm}$ is $5.55\times {10}^3\mathrm{Ohm}$.

Reason: Its resistivity is equal to $76.234\mathrm{Ohm}-\mathrm{cm}$.

• A. both assertion and reason are incorrect
• B. assertion is correct but reason is incorrect
• C. both assertion and reason are correct and reason is the correct explanation for assertion
• D. both assertion and reason are correct but reason is not correct explanation for assertion

Answer 1

The correct option is B

assertion is correct but reason is incorrect

Step 1. Given data

From the given assertion,

Molarity $\mathrm{M}=0.05\mathrm{M}$

Length, $\mathrm{l}=50\mathrm{cm}$,

Resistance, $\mathrm{R}=5.55\times {10}^3\mathrm{\Omega }$

Diameter $\mathrm{d}=1\mathrm{cm}$ and radius is $0.5\mathrm{cm}$.

From the given reason, the resistivity is equal to $76.234\mathrm{Ohm}-\mathrm{cm}$.

To find out whether the resistivity is equal to $76.234\mathrm{Ohm}-\mathrm{cm}$ or not, we have to calculate the resistivity first as per the given data.

Step 2. Formula to be used

The formula for area of circle is,

$\mathrm{A}={\mathrm{\pi r}}^2$

Here, $\mathrm{A}$ is area and $\mathrm{r}$ is radius.

The formula for resistance is,

$\mathrm{R}=\frac{\mathrm{\rho l}}{\mathrm{A}}$

So, the resistivity is calculated as,

$\mathrm{\rho }=\frac{\mathrm{R}\times \mathrm{A}}{\mathrm{l}}$

Here, $\mathrm{\rho }$ is resistivity, $\mathrm{l}$ is length, $\mathrm{R}$ is resistance and $\mathrm{A}$ is area.

Step 3. Find the cross sectional area.

We have to find the cross sectional area.

So,

$\mathrm{A}=3.14\times {\left(0.5\right)}^2$

$=0.785{\mathrm{cm}}^2$

Step 4. Calculate the resistivity.

By using the formula of resistivity, we get,

$\mathrm{\rho }=\frac{5.55\times {10}^3\times 0.785}{50}$

$=\frac{17427}{200}$

$=87.18\mathrm{\Omega }\mathrm{cm}$

Therefore, from the assertion, the resistivity is calculated as $87.18\mathrm{\Omega }\mathrm{cm}$.

Step 5. Prove the assertion

As we know that, the formula of resistance is,

$\mathrm{R}=\frac{\mathrm{\rho l}}{\mathrm{A}}$

We will prove whether the assertion is true or not by checking the value of electrical resistance.

From the above calculation,

$\mathrm{\rho }=87.18\mathrm{\Omega }\mathrm{cm}$

$\mathrm{A}=0.785{\mathrm{cm}}^2$

$\mathrm{l}=50\mathrm{cm}$

Substitute all the above values in the formula of resistance, we get,

$\mathrm{R}=\frac{87.18\times 50}{0.785}$

$=\frac{4359}{0.785}$

$=5552.866$

$=5.55\times {10}^3\mathrm{\Omega }$

So, its concluded that, the assertion is correct but the reason is incorrect.

Hence, option $\mathrm{B}$ is correct answer.