Question

Assertion :One will need a very powerful crane to lift a nuclear mass of even microscopic size. Reason: The density of nucleus is very high.

Read the above assertion and reason and choose the correct option regarding it.

• A. The Assertion is correct but Reason is wrong
• B. The Assertion is wrong but Reason is correct
• C. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
• D. Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion

Answer 1

The correct option is C Both Assertion and Reason are correct and Reason is the correct explanation of Assertion

Let $V={10}^{-5}c{m}^3$ represent the microscopic size.
The mass of this particle in nucleus = volume of particle \times density of nucleus
$Densityofnucleus=\frac{Massofnucleus}{Volumeofnucleus}$
$=\frac{A\times 1.66\times {10}^{-24}}{\frac{4}{3}\pi r^3}$
$=\frac{A\times 1.66\times {10}^{-24}}{4/3\times 3.14\times (1.33\times {10}^{-13}\times A^{1/3}{)}^3}$
$=\frac{1.66\times {10}^{-24}\times 3}{4\times 3.14\times 2.35\times {10}^{-39}}$
$=1.68\times {10}^{14}$
Thus, $massofparticle={10}^{-5}\times 1.68\times {10}^{14}g=1.68\times {10}^{9}g=1.68\times {10}^{6}kg$
As the density of nucleus is very high, One will need a very powerful crane to lift a nuclear mass of even microscopic size.
Thus, Both A and R are correct and R is correct explanation of A.