NEB Class 12 Science Physics (NEB Released Items) Question Paper 2081 (Set A) Nepal

A) Bernoulli's Principle (2 marks)

Statement: For the streamline flow of an ideal (non-viscous, incompressible) fluid through a pipe of non-uniform cross-section, the total energy of the fluid per unit volume (pressure energy + kinetic energy + potential energy) remains constant.

Example (any one): the lift on an aerofoil (aeroplane wing), the working of an atomizer/spray, or the blowing off of a roof in a strong wind.

B) Surface energy and surface tension (3 marks)

Definition: Surface energy is the amount of work done in increasing the surface area of a liquid by unit area at constant temperature.

Derivation: Consider a liquid film stretched on a wire frame with a movable wire of length $l$. The force on the wire due to surface tension $T$ (acting on both surfaces of the film) is $F = T \cdot l$ (for a single surface $F = T\,l$).

If the wire is pulled through a small distance $d$, the work done is

The increase in surface area is $A = l \cdot d$. Therefore the surface energy (work done per unit increase in area) is

Hence the surface energy per unit area is numerically equal to the surface tension: $\boxed{\sigma = T}$.

A) Doppler effect for sound (3 marks)

Let $V$ be the speed of sound, $V_s$ the speed of the source (police car), and the observer at rest ($V_0 = 0$). The emitted frequency is $f$.

i) Source moving towards a stationary observer: The wavefronts are compressed, so the apparent wavelength decreases and the apparent frequency increases:

Since $V - V_s < V$, we get $f' > f$ (higher pitch). [1]

Source moving away from a stationary observer: The wavefronts are spread out, so the apparent frequency decreases:

Since $V + V_s > V$, we get $f' < f$ (lower pitch). [1] (Description/figure of source approaching observer with velocity $V_s$, $V_0 = 0$.) [1]

ii) Both source and observer at rest (1 mark): No, there is no change in the observed frequency. When both source and observer are at rest there is no relative motion between them, so the observer hears the original frequency $f$.

iii) Pitch of approaching car rising (1 mark): As the car approaches, $f' = \left(\dfrac{V}{V - V_s}\right)f$ with $(V - V_s) < V$, so $f' > f$. The apparent frequency (pitch) is higher than the actual frequency, hence the pitch seems to rise.

B) Open pipe closed at one end (2 marks)

Fundamental frequency of an open organ pipe: $f = \dfrac{v}{2l}$.

Fundamental frequency of a closed organ pipe (closed at one end): $f' = \dfrac{v}{4l}$.

Therefore $f' = \dfrac{f}{2}$ — the fundamental frequency is reduced to half. [1+1]

C) Closed or open pipe? (1 mark)

Given $f_1 = 150\ \text{Hz}$ and the first overtone $f_2 = 450\ \text{Hz}$.

A closed pipe contains only odd harmonics, so its first overtone is the 3rd harmonic ($3f_1$). Since the ratio is 3, this is a closed organ pipe.