PHYSICS TRAIL QUESTIONS✍️ 1) State the dimensions of the following physical quantities (a) Acceleration (b) Pressure (c) Density 2) A projectile is launched with a velocity of 42ms-1 at an angle of 30o to the horizontal. If the time of flight is 4.2 s, calculate the maximum attainable height. [g = 10 ms-2] 3) Explain why mercury does not wet glass while water does 4) Explain the following terms (a) Tensile stress (b) Young’s modulus 5) An electron of charge 1.60 x 10-19C is accelerated under a potential difference of 1.0 x 105V. Calculate the energy of the electron in joules. 6). Give three observations in support of de Broglie’s assumption that moving particles behave like waves. 7(a)i) Explain relative motion ii) Two cars moving in opposite directions on the same straight road with velocities 80kmh-1 and 60kmh-1 respectively pass each other at a point. Determine the velocity of the first car relative to the second car. (b)i) Define force. ii) Classify the following forces as either contact forces or field forces: push; tension; gravitational force; electrostatic force; reaction and magnetic force. (c)A body starts from rest and travels in a straight line 2 s with uniform acceleration of 1 ms-2. It then travels at a constant speed for sometime before coming to rest with a uniform retardation of 2 ms-2. The total distance covered by it is 15m. (i) Draw and label a velocity-time graph for the motion. (ii) Calculate the: (α) Velocity attained at the end of 2 s (β) Total time taken for the journey

Velocity has dimensions of length per unit time ($L T^{-1}$), and time has dimensions of $T$.

The dimensions of acceleration are $\boxed{L T^{-2}}$.

b) Pressure

Force has dimensions of mass times acceleration ($M L T^{-2}$), and area has dimensions of length squared ($L^2$).

The dimensions of pressure are $\boxed{M L^{-1} T^{-2}}$.

c) Density

Mass has dimensions of $M$, and volume has dimensions of length cubed ($L^3$).

The dimensions of density are $\boxed{M L^{-3}}$.

Initial velocity, $u = 42 \text{ ms}^{-1}$
Angle of projection, $\theta = 30^\circ$
Acceleration due to gravity, $g = 10 \text{ ms}^{-2}$

The maximum attainable height is $\boxed{22.05 \text{ m}}$.

Mercury does not wet glass because the cohesive forces (forces between mercury molecules) are much stronger than the adhesive forces (forces between mercury molecules and glass molecules). This causes mercury to minimize its contact with the glass, forming spherical droplets. Water, on the other hand, wets glass because its adhesive forces with glass are stronger than its cohesive forces, allowing it to spread out over the surface.

a) Tensile stress
Tensile stress is the internal restoring force per unit cross-sectional area of a body when it is subjected to an external deforming force that tends to increase its length. It is calculated as the applied force divided by the cross-sectional area.

b) Young’s modulus
Young's modulus is a measure of the stiffness of an elastic material. It is defined as the ratio of tensile stress to tensile strain within the elastic limit of the material. It quantifies the material's resistance to elastic deformation under tension or compression.

Charge of electron, $q = 1.60 \times 10^{-19} \text{ C}$
Potential difference, $V = 1.0 \times 10^5 \text{ V}$

The energy of the electron is $\boxed{1.60 \times 10^{-14} \text{ J}}$.

Three observations in support of de Broglie’s assumption that moving particles behave like waves are:

• Electron diffraction: Electrons, when passed through a crystal lattice, produce diffraction patterns similar to those produced by X-rays, demonstrating their wave-like nature.
• Neutron diffraction: Neutrons also exhibit diffraction when scattered by crystalline materials, confirming their wave properties.
• Atomic interference experiments: Experiments with atoms and molecules (like C60 fullerenes) showing interference patterns further support the wave-particle duality of matter.

7(a)i)
Relative motion refers to the motion of an object as observed from a particular reference frame. It describes how the position, velocity, or acceleration of an object appears to an observer who might also be in motion.

7(a)ii)

Velocity of the first car, $v_1 = 80 \text{ kmh}^{-1}$
Velocity of the second car, $v_2 = 60 \text{ kmh}^{-1}$
Since they are moving in opposite directions, we can assign one direction as positive and the other as negative. Let $v_1$ be positive.

When objects move in opposite directions, their relative speed is the sum of their individual speeds.

The velocity of the first car relative to the second car is $\boxed{140 \text{ kmh}^{-1}}$.

7(b)i)
Force is a push or a pull that can cause an object to accelerate, decelerate, change direction, or deform. It is a vector quantity, having both magnitude and direction.

7(b)ii)

• Push: Contact force
• Tension: Contact force
• Gravitational force: Field force
• Electrostatic force: Field force
• Reaction: Contact force
• Magnetic force: Field force

7(c)i)
Velocity-time graph for the motion:
The graph will consist of three segments:

1. An upward sloping line from $t=0$ to $t=2 \text{ s}$ (uniform acceleration).
2. A horizontal line for some time (constant speed).
3. A downward sloping line until velocity becomes zero (uniform retardation).

7(c)ii)
(α) Velocity attained at the end of 2 s

Initial velocity, $u = 0 \text{ ms}^{-1}$ (starts from rest)
Acceleration, $a = 1 \text{ ms}^{-2}$
Time, $t = 2 \text{ s}$

The velocity attained at the end of 2 s is $\boxed{2 \text{ ms}^{-1}}$.

(β) Total time taken for the journey

The initial velocity for the third phase is the velocity attained at the end of the first phase, $u_3 = 2 \text{ ms}^{-1}$.
The final velocity for the third phase is $v_3 = 0 \text{ ms}^{-1}$ (comes to rest).
Retardation, $a_3 = -2 \text{ ms}^{-2}$.
Using $v = u + at$:

Using $v^2 = u^2 + 2as$:

Total distance, $S = 15 \text{ m}$.

During the second phase, the speed is constant at $2 \text{ ms}^{-1}$.

The total time taken for the journey is $\boxed{9 \text{ s}}$.