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.

Explanation

 The vertical component of velocity becomes zero at maximum height (because the ball stops rising).  

- But the horizontal component of velocity remains constant (since no air resistance).  

- So, the resultant velocity is equal to the horizontal component, which is less than the initial velocity but not zero.

Explanation

 When the cannon fires the shell forward, the shell exerts an equal and opposite force backward on the cannon (action-reaction pair).  

- This backward movement of the cannon is called recoil.  

So, recoil is a direct result of Newton’s third law of motion (for every action, there is an equal and opposite reaction).

Explanation

- Sun is the primary source of energy for Earth.

- It emits electromagnetic radiation (sunlight) that reaches Earth and provides energy for processes like climate, weather, photosynthesis, and heating.

- Wind and water (like rivers or oceans) get their energy indirectly from the Sun because solar energy drives evaporation, temperature differences, and air movement.

- Moon reflects sunlight but provides negligible energy compared to the Sun.

Explanation

- Degrees and radians are two units to measure angles.

- The relationship between degrees and radians is:  

  180 degrees = π radians

- To convert degrees to radians, use the formula:  

  radians = (π / 180) × degrees

- Given phase difference = 90°

- Convert to radians:  

  radians = (π / 180) × 90 = (π × 90) / 180 = π / 2

So, 90° = π/2 radians.