Explanation

- Gamma rays have the highest frequency and shortest wavelength in the electromagnetic spectrum.

- This gives them the greatest energy and strongest penetrating power.

- They are used in cancer treatment and come from radioactive decay.

Explanation

Thus, the First law of thermodynamics furnishes the relationship between:

• heat
• work
• the internal energy of the system

Explanation

The total energy E in simple harmonic motion (SHM) is given by:

E = (1/2) k A²

Where:  

- k is the spring constant  

- A is the amplitude

This indicates that energy is proportional to the square of the amplitude.  

Frequency and time period do not affect total energy (though they relate to speed), and wavelength is not relevant in SHM (it applies to waves).

Explanation

Protons repel each other due to their positive charges (electromagnetic force), but the strong nuclear force binds them tightly inside the nucleus, overcoming this repulsion.

Explanation

The electric field E due to an infinite charged sheet is given by:

E = σ / (2ε₀)

Where:  

- σ = surface charge density  

- ε₀ = permittivity of free space

Since E is directly proportional to σ, if the surface charge density increases by 25%, the electric field also increases by 25%.

Explanation

According to the principle of continuity for incompressible fluids:

A₁v₁ = A₂v₂

Where:  

- A = cross-sectional area  

- v = fluid speed

When the pipe becomes narrower (A decreases), the fluid speed (v) must increase to keep A × v (volume flow rate) and hence mass flow rate constant

Explanation

The curved shape of the airplane wing (airfoil) causes the air to move faster over the top surface, which according to Bernoulli’s principle results in lower pressure on the top compared to the bottom.

This pressure difference creates lift, allowing the airplane to fly

Explanation

In a pipe of varying cross-section as fluid enters the narrower region, it exhibits high velocity low pressure. 

According to Bernoulli's principle, when a fluid flows through a pipe with a decreasing cross-section (narrowing), its velocity increases, but the pressure simultaneously decreases. 

Explanation

The half-life is the time required for half of the radioactive nuclei in a sample to decay

. It is a characteristic property of each radioactive isotope.

Explanation

The Balmer series corresponds to electron transitions in the hydrogen atom where electrons fall from higher energy levels (n ≥ 3) down to the energy level n = 2.

- The energy difference in these transitions emits light in the visible spectrum.

- Other series like Lyman appear in the ultraviolet region, Paschen in the infrared, etc.