The Solid State

Step 1: {Apply shell theorem}
The shell theorem states that a uniform spherical shell of mass exerts zero net gravitational force on a particle inside it.
Step 2: {Explain force cancellation}
Forces from opposite sides of the shell cancel out due to symmetry, leaving: Net gravitational force = 0.
Thus, the correct answer is zero.

Step 1: {Understanding the Logic Circuit}
The circuit consists of two NOR gates whose outputs are given as inputs to another NOR gate.
Step 2: {Boolean Expression}
Using De-Morgan’s theorem:
Step 3: {Conclusion}
The circuit implements an AND gate. Thus, the correct answer is (B).

Step 1: {Understanding Zener Diode}
A zener diode allows current to flow in the reverse direction when the applied voltage exceeds the breakdown voltage.
Step 2: {Function of a Zener Diode}
In the breakdown region, the voltage across the diode remains nearly constant, making it ideal for voltage regulation. Thus, the correct answer is (C).

Step 1: {Understanding the Circuit}
The circuit consists of NOT gates applied to and , followed by an AND gate.
Step 2: {Boolean Expression Derivation}
Applying De-Morgan's theorem:
Step 3: {Conclusion}
The output matches the OR gate. Thus, the correct answer is (B).

Step 1: {Understanding Binding Energy per Nucleon}
The binding energy per nucleon ( ) is the energy required to disassemble a nucleus into its constituent protons and neutrons. It is an important measure of nuclear stability. The higher the binding energy per nucleon, the more stable the nucleus is. The binding energy per nucleon is typically highest for elements in the mid-range of the periodic table, particularly for elements around iron ( ).
Step 2: {Comparing the Nuclei}
- Lighter nuclei, such as (Helium-4), have a relatively low binding energy per nucleon. This is because the nucleons in lighter nuclei are not as tightly bound as in heavier nuclei.
- Heavy nuclei, such as (Lead-208), also tend to have lower binding energy per nucleon compared to mid-range nuclei. This is due to the electrostatic repulsion between the positively charged protons, which weakens the nuclear force that binds the nucleus together.
- (Iron-56), which has the highest binding energy per nucleon (around 8.8 MeV), is considered the most stable nucleus. This high binding energy per nucleon explains why nuclear fusion (such as in stars) generally produces energy by fusing lighter elements up to iron, and why fission of heavy elements releases energy. Thus, the correct answer is .