Physics entrance exam, 2017 E.C. (2025)

No outside force acts on the two blocks, so the total momentum before the collision equals the total momentum after it: \( m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2 \).

Momentum before: \( (8.0)(6.0) + (12.0)(3.0) = 48 + 36 = 84 \, \text{kg·m/s} \).

Momentum after: \( (8.0)(4.0) + 12.0\,v_2 = 32 + 12v_2 \).

Set them equal: \( 84 = 32 + 12v_2 \), so \( 12v_2 = 52 \) and \( v_2 = 4.33 \, \text{m/s} \).

The result is positive, so block B keeps moving along the positive x-direction. Options A and B fail because a positive answer cannot point along the negative x-axis.

Textbook: Physics Grade 11, Unit 4 Dynamics, section 4.6 Impulse and Linear Momentum (page 148).

A simple machine takes in work on one side and gives out work on the other side. The force you apply to the machine is called the effort, and the work it does is the input work.

The load is the force the machine works against, so it belongs to the output side, not the input side. Friction wastes some of the input work, and the normal force is a support force from a surface; neither of them is the applied force.

Textbook: Physics Grade 9, Unit 5 Simple Machines, section 5.5 Mechanical Advantage, Velocity Ratio and Efficiency (page 92).

In a longitudinal wave, the particles of the medium vibrate parallel to the direction the wave travels. Sound in air is the common example, and it is made of compressions and rarefactions.

In a transverse wave, the particles vibrate perpendicular to the direction the wave travels. A wave on a string is the common example, and it shows crests and troughs.

Option C states exactly this. Options A and D swap the two descriptions, and option B swaps the examples.

Textbook: Physics Grade 9, Unit 6 Mechanical Oscillation and Sound Wave, section 6.1 Common Characteristics of Waves (page 114).

A fluid pushes up on a submerged object with the buoyant force. Because of this upward push, the object seems lighter than it does in air.

So the apparent weight is:

\[ W_{\text{apparent}} = W_{\text{in air}} - F_{\text{buoyant}} \]

Option A describes the size of the buoyant force itself (Archimedes' principle says it equals the weight of the displaced fluid), not the apparent weight.

Textbook: Physics Grade 12, Unit 3 Fluid Mechanics, section 3.3 Archimedes' principle (page 96).

Velocity ratio of a wheel and axle is the wheel radius over the axle radius: \( \text{VR} = \frac{R}{r} = \frac{40}{8} = 5 \).

The load is the weight of the water: \( W = mg = 6 \times 10 = 60 \, \text{N} \). The actual mechanical advantage is \( \text{AMA} = \frac{\text{load}}{\text{effort}} = \frac{60}{20} = 3 \).

Efficiency compares the two:

\[ \eta = \frac{\text{AMA}}{\text{VR}} \times 100\% = \frac{3}{5} \times 100\% = 60\% \]

Textbook: Physics Grade 9, Unit 5 Simple Machines, section 5.5 Mechanical Advantage, Velocity Ratio and Efficiency (page 92).

A current in a long straight wire creates a magnetic field whose lines are circles centered on the wire. The right-hand rule shows the direction: point the thumb along the current and the curled fingers give the circular field direction.

The field strength is \( B = \frac{\mu_0 I}{2\pi r} \). It grows with the current (so D is wrong) and gets weaker as you move away from the wire (so C is wrong). The field is not along the current; it circles around it (so A is wrong).

Textbook: Physics Grade 10, Unit 5 Magnetism, section 5.4 Magnetic field of a current carrying conductor.