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Which of the following statements about the universal gravitational constant (G) is correct?
The term 'universal gravitational constant' itself implies that G is constant throughout the universe and does not depend on the specific masses or the medium. The text uses a single value for G in all calculations, reinforcing its universal nature.
The formula for acceleration due to gravity on the Earth's surface, $g = GM_E / R_E^2$, clearly shows the relationship between 'g', the Earth's mass ($M_E$), its radius ($R_E$), and the universal gravitational constant (G). This equation implicitly suggests that:
From Eq. (7.12), $g = GM_E / R_E^2$, it is clear that 'g' is directly proportional to both G and $M_E$ and inversely proportional to the square of $R_E$.
Which of the following projectiles would be most suitable to accurately measure the sizes of nuclei, especially when short-range nuclear forces start to affect scattering?
The NCERT states, 'By performing scattering experiments in which fast electrons, instead of a-particles, are projectiles that bombard targets made up of various elements, the sizes of nuclei of various elements have been accurately measured.' This is because electrons are not subject to the strong nuclear force, allowing for more precise measurements based on electromagnetic interactions only.
According to Rutherford's calculations, a deviation from pure Coulomb repulsion in alpha-particle scattering indicates the influence of:
The NCERT text states, 'the scattering will begin to be affected by the short range nuclear forces, and differ from Rutherford’s calculations. Rutherford’s calculations are based on pure coulomb repulsion between the positive charges of the a-particle and the gold nucleus.' This deviation from Coulomb repulsion signifies the involvement of the strong nuclear force at very close distances.
If the radius of a nucleus with mass number A is given by $R = R_0 A^{1/3}$, what is the approximate value of $R_0$?
The NCERT text specifies, 'It has been found that a nucleus of mass number A has a radius $R = R_0 A^{1/3}$ where $R_0 = 1.2 \times 10^{-15} \text{ m} (=1.2 \text{ fm})$.'
Based on the formula $R = R_0 A^{1/3}$, the volume of a nucleus is directly proportional to its:
The text states, 'This means the volume of the nucleus, which is proportional to $R^3$ is proportional to A.' Since $R \propto A^{1/3}$, then $R^3 \propto (A^{1/3})^3 \propto A$.
What is the approximate density of nuclear matter?
The NCERT states, 'The density of nuclear matter is approximately $2.3 \times 10^{17} \text{ kg m}^{-3}$.'
The extremely high density of nuclear matter compared to ordinary matter, like water, suggests that:
The text explains this high density by saying, 'This is understandable, as we have already seen that most of the atom is empty. Ordinary matter consisting of atoms has a large amount of empty space.' The vast emptiness of the atom means its mass is concentrated in a tiny, dense nucleus.
In Rutherford's alpha-particle scattering experiment, what was the primary reason for using a thin gold foil?
The NCERT states, 'As the gold foil is very thin, it can be assumed that a-particles will suffer not more than one scattering during their passage through it. Therefore, computation of the trajectory of an alpha-particle scattered by a single nucleus is enough.'
What is the approximate range for the diameter of an atom as determined from kinetic theory?
The text mentions, 'From kinetic theory, the size of an atom was known to be $10^{-10} \text{ m}$'.
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The bank mixes NEET previous year questions (PYQs) with practice questions, each tagged with its exam appearances where applicable.