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.

Explanation

An angular displacement of 90° is:

- 1 complete revolution = 360°  

- So, 90° = 90/360 = 1/4 revolution

Explanation

In an ideal transformer:

Vₚ / Vₛ = Nₚ / Nₛ (Voltage ratio = turns ratio)

And power is conserved:  

Pₚ = Pₛ → Vₚ Iₚ = Vₛ Iₛ

If primary voltage (Vₚ) is doubled and turns ratio remains the same, then:

- Secondary voltage (Vₛ) also doubles (because turns ratio same).

- Power input doubles (assuming the same current on primary).

To keep power balanced, if secondary voltage doubles, then:

Iₛ = (Vₚ Iₚ) / Vₛ

Since Vₚ doubles and Vₛ doubles, secondary current remains the same (assuming primary current remains same).

Explanation

Given:  

- P = momentum  

- m = mass  

We know:  

Kinetic Energy (K.E.) = (1/2)mv²  

And P = mv ⇒ v = P/m

Substitute in K.E. formula:  

K.E. = (1/2) * m * (P/m)² = (1/2) * m * (P² / m²) = P² / (2m)

Explanation

- Two equal and opposite charges produce E = 100 N/C at a point.  

- If magnitude of each charge is doubled, what is the new electric field?

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Electric field (E) due to a point charge is directly proportional to the magnitude of the charge:  

E ∝ q

If both charges are doubled, the net electric field at that point also doubles.

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So, New Electric Field = 2 × 100 N/C = 200 N/C

Explanation

- A plastic sheet with relative permittivity εᵣ = 2.5 is inserted between two point charges.  

- Initially, they are in vacuum.

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Electrostatic force (F) in a medium:  

F = (1 / 4πε₀εᵣ) * (q₁q₂ / r²)  

Compared to vacuum:  

F_medium = F_vacuum / εᵣ

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So the force decreases by a factor equal to εᵣ.

Explanation

The formula for the horizontal range R of a projectile is:

R = (u² * sin 2θ) / g

- Maximum range occurs at θ = 45°, so max range R_max = (u²)/g

- If range becomes half of max range:  

  R = (1/2) * R_max  

  => sin 2θ = 1/2 * sin 90° = 1/2

- So, sin 2θ = 1/2 → 2θ = 30° or 150°

- Therefore, θ = 15° or 75°

From the options, 15° fits.