Explanation

The sentence starts with "After he had researched," which is past perfect tense. The correct structure to follow is:

"had + past participle" → "had researched and written".

Explanation

In uniform circular motion, there is no angular acceleration (α = 0).

Since torque τ = Iα, and α = 0, torque is zero (τ = 0 Nm).

Explanation

Flammable : Burn → Something flammable is likely to burn.

Fragile : Break → Something fragile is likely to break.

Explanation

Work done = F × d × cos(θ); when angle θ = 180°, cos(180°) = -1.

So, if force and displacement are antiparallel (opposite), the work is negative.

Explanation

She told the doctor that she would be going to Murree the next day.

"Said to" changes to "told" and "will" changes to "would" in indirect speech.

"Tomorrow" becomes "the next day" as per rules of reported speech.

Explanation

For the X and Y components of a force to be equal:

Fx = Fy

Given F = Fx i + Fy j = F cos(θ) i + F sin(θ) j

Fx = F cos(θ)

Fy = F sin(θ)

For Fx = Fy:

F cos(θ) = F sin(θ)

cos(θ) = sin(θ)

tan(θ) = 1

θ = 45°

Explanation

The Earth bulges at the equator and rotates, creating a centrifugal force that slightly reduces gravity there.

At the poles, this effect is minimal, so ‘g’ is stronger at the poles than at the equator.

Explanation

The sound level β (in dB) is given by:

β = 10 log(I / I₀)

where I₀ is the threshold intensity (faintest audible sound). Given I = I₀:

β = 10 log(1) = 0 dB

Explanation

The phrase "eating out" means having a meal outside the home, usually at a restaurant.

So, "We are eating out tonight" is correct.

Explanation

Kinetic energy (K) is related to momentum (p) by K = p² / 2m. If momentum increases by 20%, the new momentum p' = 1.2p.

The new kinetic energy K' = (p')² / 2m = (1.2p)² / 2m = 1.44p² / 2m = 1.44K.

The percentage increase in K.E is ((K' - K) / K) × 100 = ((1.44K - K) / K) × 100 = 44%.