Which chapter is costing you marks?

Answer: R/9.

Each piece has length L/3, so resistance R/3. Three pieces of R/3 in parallel:

General rule: cut into n pieces and connect in parallel → R_eq = R/n².

Each piece has one third the length, so resistance R/3. Three of them in parallel give (R/3)/3 = R/9. Option R/3 stops after the cut; 3R treats them as a series combination.

Answer: the 60 W lamp.

Compute each lamp's resistance from its rating:

In SERIES the two lamps carry the SAME current, so the relevant power formula is P = I²R and brightness now goes with resistance:

So the 60 W lamp — the one with higher resistance — dissipates more power and glows brighter, the exact reverse of their behaviour in parallel.

This is a classic reversal question. The lesson is to choose the power formula that holds the SHARED quantity fixed: use P = V²/R when the voltage is common (parallel) and P = I²R when the current is common (series). Neither lamp reaches its rated brightness here, since they share the 220 V between them.

Answer: increases.

With the battery disconnected the CHARGE is fixed, so use the form of the energy that holds Q constant:

Increasing d reduces C, and with Q fixed the energy therefore RISES.

The extra energy comes from the work you do pulling the oppositely charged plates apart against their mutual attraction. Had the battery stayed connected, V would be fixed and the energy would instead fall.

Answer: both a net force and a torque.

In a uniform field the two charges feel equal and opposite forces that cancel:

In a NON-uniform field the two forces differ in magnitude, leaving a net force as well as a torque.

This is why a charged comb attracts neutral paper: it polarises the paper and then pulls the nearer induced charge more strongly.

The dipole is drawn toward the region of stronger field.

Answer: double; double.

No external torque acts about the spin axis, so angular momentum is conserved:

The kinetic energy DOUBLES even though angular momentum is unchanged. The extra energy comes from the muscular work the skater does pulling her arms inward against the centrifugal effect.

Answer: sphere, disc, ring.

The acceleration depends only on the shape factor I/MR²:

The values are 2/5, 1/2 and 1 for sphere, disc and ring, so the sphere has the largest acceleration.

Mass and radius cancel entirely — a marble and a cannonball of the same shape arrive together.

Answer: increases.

The lensmaker's equation uses the RELATIVE refractive index:

In water the ratio falls from about 1.5 to roughly 1.13, so the bracket shrinks and f grows.

The lens converges more weakly because the contrast in refractive index across its surfaces is reduced.

If the surrounding medium were denser than the lens, a convex lens would actually diverge light.

Answer: red.

The refractive index falls with increasing wavelength:

Red light has the smallest μ, so (μ − 1) is smallest and f is largest.

Violet is therefore focused closest to the lens, and this spread of focal points is chromatic aberration.

Answer: the number of photoelectrons per second.

Intensity measures how many photons arrive per second, and each photon ejects at most one electron:

So brighter light gives a larger saturation current but leaves the stopping potential unchanged.

Separating 'how many' from 'how energetic' is the central insight that classical wave theory could not supply.

Answer: the same momentum but different energy.

Both obey the de Broglie relation:

Equal wavelength therefore means equal momentum.

Their energies differ completely: the photon has E = pc while the electron has E = p²/2m non-relativistically.

This contrast neatly illustrates that momentum and energy are related differently for massless and massive particles.