Read the following statements:
(A) Volume of the nucleus is directly proportional to the mass number.
(B) Volume of the nucleus is independent of mass number.
(C) Density of the nucleus is directly proportional to the mass number.
(D) Density of the nucleus is directly proportional to the cube root of the mass number.
(E) Density of the nucleus is independent of the mass number.
Choose the correct option from the following options

Question

Two solid spheres each of mass 2 kg and radius 75 cm are arranged as shown. Find MOI of the system about the given axis.

Answer 1

The question requires us to evaluate several statements regarding the volume and density of atomic nuclei in relation to the mass number.

First, let's analyze the given statements:

(A) Volume of the nucleus is directly proportional to the mass number.
- The volume of a nucleus is typically considered to be proportional to the (A^{1/3}) (where A is the mass number) because the radius R of a nucleus is given by R = R_0 A^{1/3}. Therefore, the volume (V = \frac{4}{3}\pi R^3) is proportional to A. This statement is true.
(B) Volume of the nucleus is independent of mass number.
- This statement contradicts (A), as established that volume is proportional to mass number A^{1/3}. Therefore, it is false.
(C) Density of the nucleus is directly proportional to the mass number.
- The density of a nucleus is given by \text{Density} = \frac{\text{Mass}}{\text{Volume}}. Since both mass and volume are proportional to A, the density is independent of mass number. Therefore, this statement is false.
(D) Density of the nucleus is directly proportional to the cube root of the mass number.
- This statement is also incorrect as the density remains constant irrespective of the mass number, contradicting with the proportionality suggested in (D).
(E) Density of the nucleus is independent of the mass number.
- This statement is true as the nuclear density remains approximately constant regardless of mass number due to both mass and volume increasing proportionally.

Based on the analysis above, the correct statements are (A) and (E).

Therefore, the correct option is: (A) and (E) only.

Answer 2

The question requires us to evaluate several statements regarding the volume and density of atomic nuclei in relation to the mass number.

First, let's analyze the given statements:

(A) Volume of the nucleus is directly proportional to the mass number.
- The volume of a nucleus is typically considered to be proportional to the (A^{1/3}) (where A is the mass number) because the radius R of a nucleus is given by R = R_0 A^{1/3}. Therefore, the volume (V = \frac{4}{3}\pi R^3) is proportional to A. This statement is true.
(B) Volume of the nucleus is independent of mass number.
- This statement contradicts (A), as established that volume is proportional to mass number A^{1/3}. Therefore, it is false.
(C) Density of the nucleus is directly proportional to the mass number.
- The density of a nucleus is given by \text{Density} = \frac{\text{Mass}}{\text{Volume}}. Since both mass and volume are proportional to A, the density is independent of mass number. Therefore, this statement is false.
(D) Density of the nucleus is directly proportional to the cube root of the mass number.
- This statement is also incorrect as the density remains constant irrespective of the mass number, contradicting with the proportionality suggested in (D).
(E) Density of the nucleus is independent of the mass number.
- This statement is true as the nuclear density remains approximately constant regardless of mass number due to both mass and volume increasing proportionally.

Based on the analysis above, the correct statements are (A) and (E).

Therefore, the correct option is: (A) and (E) only.

The Correct Option is B