Explanation

• A velocity–time graph shows how velocity changes with time.
• The slope gives acceleration.
• The area under the graph represents motion covered.
• It connects velocity with displacement.

Last verified on 22-05-2026

Explanation

• Escape velocity is √2 times orbital velocity.
• So, a body needs about 1.414 times more speed to escape than to orbit.
• This comes from gravitational energy requirements.

Additional information:

• Orbital speed near Earth: ~7.9 km/s
• Escape velocity near Earth: ~11.2 km/s
• Ratio: vₑ : v₀ = √2 : 1

Last verified on 22-05-2026

Explanation

• Energy stored in a capacitor is given by: U = Q² / (2C)
• This comes from integrating work done to move charge onto the capacitor plates.
• It shows energy increases with square of charge and decreases with capacitance.

Last verified on 22-05-2026

Explanation

• Nuclear fission is the splitting of a heavy nucleus into lighter nuclei.
• It usually occurs in elements like Uranium-235.
• During fission, a small amount of mass is converted into energy.
• This energy is released according to Einstein’s equation E = mc².
• It produces a large amount of energy used in nuclear power plants.

Last verified on 22-05-2026

Explanation

• Radioactive decay follows an exponential law.
• Decay constant (γ) shows how fast a nucleus decays.
• Mean life (τ) is the average lifetime of a radioactive nucleus.
• Both quantities are inversely related.
• Greater decay constant means shorter mean life.

Last verified on 22-05-2026

Explanation

• Alpha decay is a type of radioactive decay of heavy nuclei.
• In this process, an alpha particle (⁴₂He) is emitted.
• The nucleus loses 2 protons and 2 neutrons.
• This reduces both mass number and atomic number.
• It commonly occurs in very heavy elements like uranium.

Last verified on 22-05-2026

Explanation

• Beta minus (β⁻) decay is a type of radioactive decay.
• It occurs when a neutron changes into a proton inside the nucleus.
• During this process, a beta particle (electron) is emitted.
• An antineutrino is also released for energy balance.
• Atomic number increases by 1 after decay.

Last verified on 22-05-2026

Explanation

• Refractive index describes how light slows down in a medium compared to vacuum.
• It is a measure of bending of light when it enters another medium.
• Formula: n = c / v
• It has no unit (dimensionless quantity).
• Higher refractive index means more bending of light.

Last verified on 22-05-2026

Explanation

In series combination of capacitors:

1/C = 1/C1 + 1/C2

1/C = 1/2 + 1/3

1/C = (3 + 2) / 6 = 5/6

So, C = 6/5 = 1.2 μF

Last verified on 22-05-2026

Explanation

Substitute values:

1/R = 1/3 + 1/6

1/R = (2 + 1) / 6 = 3/6 = 1/2

So, R = 2 Ω

Last verified on 22-05-2026