NSAA 2019 Advanced Mathematics And Advanced Physics PART E

• A.4
• B.12
• C.21
• D.25
• E.27
• F.30

Answer: C

• A.$6.48 \times 10^4 \text{ m}^3$
• B.$7.20 \times 10^4 \text{ m}^3$
• C.$8.00 \times 10^4 \text{ m}^3$
• D.$6.48 \times 10^7 \text{ m}^3$
• E.$7.20 \times 10^7 \text{ m}^3$
• F.$8.00 \times 10^7 \text{ m}^3$

Answer: C

• A.-9
• B.-3
• C.-1
• D.1
• E.3
• F.9

Answer: B

A car P of mass 1000 kg is travelling north at $30\text{ms}^{-1}$ along a straight, horizontal road when it hits another car Q which is directly ahead of P and travelling in the same direction. Car Q has a mass of 500 kg and is travelling at $20 \text{ms}^{-1}$.

The collision lasts for 0.20 s and immediately after the collision car Q is moving north at $30 \text{ms}^{-1}$.

What is the speed of P immediately after the collision and what is the size of the average resultant force that acts on Q during the collision?

(Assume that no external forces act on the cars during the collision.)

• A.speed of P: $20 \text{ms}^{-1}$, average force on Q: $25000 \text{N}$
• B.speed of P: $20 \text{ms}^{-1}$, average force on Q: $50000 \text{N}$
• C.speed of P: $20 \text{ms}^{-1}$, average force on Q: $100000 \text{N}$
• D.speed of P: $20 \text{ms}^{-1}$, average force on Q: $125000 \text{N}$
• E.speed of P: $25 \text{ms}^{-1}$, average force on Q: $25000 \text{N}$
• F.speed of P: $25 \text{ms}^{-1}$, average force on Q: $50000 \text{N}$
• G.speed of P: $25 \text{ms}^{-1}$, average force on Q: $100000 \text{N}$
• H.speed of P: $25 \text{ms}^{-1}$, average force on Q: $125000 \text{N}$

Answer: E

• A.$\frac{1}{2}$ or $\frac{1}{3}$
• B.$\frac{1}{\sqrt{3}}$ or $\frac{1}{2\sqrt{2}}$
• C.$\frac{\sqrt{3}}{2}$ or $\frac{2\sqrt{2}}{3}$
• D.$\sqrt{3}$ or $2\sqrt{2}$
• E.3 or 2

Answer: D

• A.0.05 V
• B.0.20 V
• C.0.80 V
• D.3.2 V
• E.5.0 V
• F.20 V

Answer: C

An equilateral triangle of side 8 cm is drawn so that its vertices lie on the circumference of a circle, as shown in the diagram.

[Image of a circle with an inscribed equilateral triangle. The side length of the triangle is labeled '8 cm'. The three segments of the circle that are outside the triangle are shaded.]

What is the total of the three areas shaded in the diagram, in $\text{cm}^2$?

• A.$8(2\pi - 3)$
• B.$24(\pi - \sqrt{3})$
• C.$48(4\pi - \sqrt{3})$
• D.$\frac{16}{3}(4\pi - 6 - 3\sqrt{3})$
• E.$\frac{16}{3}(4\pi - 3\sqrt{3})$

Answer: E

A uniform square trap door of side 0.80 m and mass 14 kg has a smooth hinge at one edge and is held open at an angle of $30^\circ$ to the horizontal. It is supported by a single rigid rod placed so that it meets the surface of the trap door at $90^\circ$ at a distance 0.10 m from the top edge of the trap door, as shown.

[Image showing a trap door hinged at the bottom left, held open at an angle of 30 degrees to the horizontal. The door is a square of side 0.80 m. A supporting rod is placed perpendicular to the trap door, meeting it at a point 0.10 m from the top edge.]

What is the normal contact force exerted on the trap door by the rod?

(gravitational field strength = $10 \text{ N kg}^{-1}$)

• A.40 N
• B.$35\sqrt{3} \text{ N}$
• C.$40\sqrt{3} \text{ N}$
• D.80 N
• E.$80\sqrt{3} \text{ N}$
• F.$\frac{280\sqrt{3}}{3} \text{ N}$

Answer: D

• A.$x = \log_5 \left( \frac{1}{3} \right)$
• B.$x = \log_5 \left( \frac{2}{5} \right)$
• C.$x = \log_5 \left( \frac{3}{5} \right)$
• D.$x = \log_5 \left( \frac{2}{3} \right)$
• E.$x = \log_5 \left( \frac{5}{3} \right)$
• F.$x = \log_5 \left( \frac{5}{2} \right)$

Answer: B

Two small loudspeakers are placed side by side 30 cm apart.

They are connected to the same signal generator so that they emit sound of frequency 400 Hz in phase with one another.

The sounds both reach a microphone placed 40 cm directly in front of one of the two loudspeakers as shown.

[Image showing two loudspeakers, one above the other, separated by a vertical distance of 30 cm. A microphone is positioned 40 cm horizontally from the lower loudspeaker, such that the line connecting the microphone and the lower loudspeaker is perpendicular to the line connecting the two loudspeakers.]

What is the phase difference between waves from the loudspeakers as they arrive at the microphone?

(speed of sound = $320 \text{ms}^{-1}$)

• A.$30^\circ$
• B.$36^\circ$
• C.$45^\circ$
• D.$60^\circ$
• E.$72^\circ$
• F.$90^\circ$
• G.$120^\circ$

Answer: C