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

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 n + l rule helps determine the energy of orbitals, where n = principal quantum number and l = azimuthal quantum number.

For 3p orbital, n = 3 and l = 1, so n + l = 4, matching the given condition.

Explanation

Time period T = 1/frequency 1/0.5 = 2 seconds.

The time period is the time taken for one complete oscillation.

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%.

Explanation

A D.C. generator uses split rings (commutator) to reverse the current direction in the coil every half rotation.

This ensures that the output current flows in one direction (direct current).

Explanation

According to the law of reflection, angle of incidence = angle of reflection.

So, if light strikes at 30°, it reflects at 30°.

Explanation

Power = 1/f (in meters)

f = 8 cm = 0.08 m

Power = 1/0.08 = 12.5 D

Explanation

If the original cable breaks at a stretch of 2 mm, each half will have half the length and thus half the maximum stretch:

Maximum stretch for half = 2 mm / 2 = 1 mm.

Explanation