Question

Assertion : A shot put is metallic sphere of radius $4\mathrm{cm}$. If the density of the metal is $10\mathrm{g}$ per ${\mathrm{cm}}^3$, then the mass of the shot put is $2\mathrm{kg}$.

Reason: Volume of sphere of radius $r$ is $\frac{4}{3}\pi r^3$.

Which of the following is correct?

• A. If both assertion and reason are true and reason is the correct explanation of assertion.
• B. If both assertion and reason are true but reason is not the correct explanation of assertion.
• C. If assertion is true but reason is false.
• D. If assertion is false but reason is true.

Answer 1

The correct option is D

If assertion is false but reason is true.

Explanation for correct option

Option D:

Assertion:

Step 1: Given data

radius of sphere$=4cm$

Density of metal$=10g/c{m}^3$

Mass of the shot put$=?$

Using the formula,

volume of sphere$=\frac{4}{3}{\mathrm{\pi r}}^3$

Calculating the mass of the shot put

We know that,

$Density=\frac{Mass}{Volume}$

Volume of sphere$=\frac{4}{3}{\mathrm{\pi r}}^3=\frac{4}{3}\times \frac{22}{7}\times 4^3$

Mass$=$Density$\times$Volume

Mass$=$$10\times \frac{4}{3}\times \frac{22}{7}\times 4^3=2681.90g$

Mass$=2681.90\times 1000=2.68kg\ne 2kg$

Thus, a shot put, radius $4\mathrm{cm}$ having metal density of $10\mathrm{g}$ per ${\mathrm{cm}}^3$, then the mass of the shot put is not $2\mathrm{kg}$.

Assertion is incorrect.

Reason:

We know that, volume of a sphere is given as,

$\frac{4}{3}\pi r^3$

Thus, volume of sphere of radius $r$ is $\frac{4}{3}\pi r^3$.

Reason is correct.

Since, Assertion is false and Reason is true.

Hence, option D is correct.