JEE MAIN - Physics (2024 - 31st January Evening Shift - No. 27)
A nucleus has mass number $$A_1$$ and volume $$V_1$$. Another nucleus has mass number $$A_2$$ and Volume $$V_2$$. If relation between mass number is $$A_2=4 A_1$$, then $$\frac{V_2}{V_1}=$$ __________.
Answer
4
Explanation
For a nucleus
Volume: $$\mathrm{V}=\frac{4}{3} \pi \mathrm{R}^3$$
$$\begin{aligned} & \mathrm{R}=\mathrm{R}_0(\mathrm{A})^{1 / 3} \\ & \mathrm{~V}=\frac{4}{3} \pi \mathrm{R}_0^3 \mathrm{A} \\ & \Rightarrow \frac{\mathrm{V}_2}{\mathrm{~V}_1}=\frac{\mathrm{A}_2}{\mathrm{~A}_1}=4 \end{aligned}$$
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