JEE Main & Advanced Sample Paper JEE Main Sample Paper-19

  • question_answer DIRECTIONS (Qs. 54): Each of these questions contains two statements: Statements -1 (Assertion) and Statement -2 (Reason). Choose the correct answer (ONLY ONE option correct) from the following.
    Statement 1: A nucleus at rest splits into two nuclear parts having radii in the ratio\[1:2\]. Their velocities will be in the ratio \[8:1\].
    Statement 2: The radius of a nucleus is proportional to the cube root of its mass number.

    A)  Statement-1 is false, Statement - 2 is true.

    B)  Statement-1 is false, Statement - 2 is true. Statement-2 is a correct explanation for Statement-1.

    C)  Statement-1 is true, Statement -2 is true; Statement -2 is not a correct explanation for Statement -1

    D)  Statement-1 is true, Statement-2 is false

    Correct Answer: A

    Solution :

     \[^{a}{{\mu }_{d}}=\sqrt{6},\,\,{{\,}^{a}}{{\mu }_{\ell }}=\sqrt{3},\] \[^{\ell }{{\mu }_{d}}=?;\,\,{{\,}^{a}}{{\mu }_{d}}{{\times }^{d}}{{\mu }_{\ell }}{{\times }^{\ell }}{{\mu }_{a}}=1\] \[\sqrt{6}{{\times }^{d}}{{\mu }_{\ell }}\times \frac{1}{\sqrt{3}}=1\] \[^{d}{{\mu }_{\ell }}=\frac{\sqrt{3}}{\sqrt{6}}=\frac{1}{\sqrt{2}};{{\,}^{\ell }}{{\mu }_{d}}=\sqrt{2}\] If C be the critical angle, then \[Sin\,\,C=\frac{1}{\mu }=\frac{1}{\sqrt{2}}\] \[C={{45}^{o}}\]. As angle of incidence\[<45{}^\circ \], it will not be internally reflected. So statement 1 is false statement 2 is true.

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