The mass number and the volume of a nucleus are $A$ and $V$ respectively. If the mass number is increased to $2A$, then the volume changes to:

$A$ nucleus has mass number $\alpha$ and radius $R_{\alpha}$. Another nucleus has mass number $\beta$ and radius $R_{\beta}$. If $\beta = 8\alpha$, then $R_{\alpha}/R_{\beta}$ is:

$A$ nucleus ruptures into two nuclear parts which have their velocity ratio equal to $2 : 1$. What will be the ratio of their nuclear size (nuclear radius)?

What is the particle $x$ in the following nuclear reaction :
${ }_4^9 Be+{ }_2^4 He \rightarrow{ }_6^{12} C+x$

Consider the following statements ($X$ and $Y$ stand for two different elements):
$(I)$ ${ }_{32}^{65} X$ and ${ }_{33}^{65} Y$ are isotopes.
$(II)$ ${ }_{42}^{86} X$ and ${ }_{42}^{85} Y$ are isotopes.
$(III)$ ${ }_{85}^{174} X$ and ${ }_{88}^{177} Y$ have the same number of neutrons.
$(IV)$ ${ }_{92}^{235} X$ and ${ }_{94}^{235} Y$ are isobars.
Which of the above statements are correct?

Which of the following pairs is an isobar?