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.

Explanation

After 3 half-lives, the remaining fraction is:

(1/2)³ = 1/8

Explanation

 m₁ = 2 kg, u₁ = 5 m/s  

- m₂ = 3 kg, u₂ = 1 m/s  

- Both moving in same direction  

- Relative speed of approach = u₁ − u₂ = 4 m/s

Explanation

F = k * (q₁q₂) / r²

Changes:  

- q₁ and q₂ → doubled → (2q)² = 4 times  

- r → halved → (½r)² = ¼  

So:  

F’ = k * (4q²) / (¼r²) = 16F

Explanation

- At launch point, both vertical and horizontal components of velocity exist.  

- At the highest point, vertical component is zero.  

- So, total velocity is maximum at launch.

Explanation

- At the midpoint, the electric fields due to each charge are equal in magnitude but opposite in direction, so they partially cancel out, making the net field weakest there.

Explanation

- Critical velocity is the maximum velocity at which fluid flows in laminar form.  

- Turbulent flow begins when the fluid exceeds this critical velocity.