2024 - JAMB Physics Past Questions and Answers - page 8

When a light ray passes from a less dense medium (air) to a denser medium (water), it bends towards the normal. This bending is called refraction. The angle of refraction (in water) will be less than the angle of incidence (in air) because the speed of light decreases in water.

Here's how to solve the problem:

• Identify the given information:
     - Wavelength (λ) = 0.25 m (distance between successive crests)
     - Frequency (f) = 4 Hz (4 oscillations per second)
• Recall the wave speed formula:
     - v = fλ, where:
        v = wave speed
        f = frequency
        λ = wavelength
• Substitute the values and calculate:
     - v = 4 Hz * 0.25 m
     - v = 1 m/s

Therefore, the speed of the wave is 1 m/s.

The gravitational force between two objects can be calculated using Newton's law of universal gravitation:

F = G * (m1 * m2) / r^2

Where:
- F is the gravitational force (6.67 N)
- G is the gravitational constant (6.6 x 10^-11 Nm²kg⁻²)
- m1 and m2 are the masses of the objects (10²⁴ kg and 10²⁷ kg)
- r is the distance between the centers of the objects (what we need to find)

1. Rearrange the formula to solve for r:
r = sqrt[ G * (m1 * m2) / F ]

2. Substitute the given values:
r = sqrt[ (6.6 x 10^-11) * (10²⁴ * 10²⁷) / 6.67 ]

3. Simplify the expression:
r ≈ sqrt[ 10⁴⁰ ]
r = 1.0 x 10²⁰ m

Therefore, the distance between the two objects is approximately 1.0 x 10²⁰ m.

The gravitational force (F) between two objects is given by Newton's law of gravitation:

F = G * (m1 * m2) / r^2

Where:
- G is the gravitational constant
- m1 and m2 are the masses of the objects
- r is the distance between the objects

If the distance (r) is halved, the new distance becomes r/2. The new force (F') can be calculated as follows:

F' = G * (m1 * m2) / (r/2)^2 = 4 * G * (m1 * m2) / r^2 = 4 * F

Since the original force F is 10N, the new force F' will be:

F' = 4 * 10N = 40N

Model rockets consist of several key components:

• Body tube: This is the main structure of the rocket.
• Nose cone: This is the front part of the rocket, designed for aerodynamics.
• Fin: These are attached to the body tube to stabilize the rocket's flight.
• Recovery devices: Parachutes or streamers are used to ensure a safe landing. The question asks what isn't a part, and recovery devices are included in the list of rocket parts.

When boiling water is poured into a thick glass tumbler, the inner surface of the glass comes into contact with the hot water and heats up rapidly, causing it to expand. However, the outer surface of the glass remains relatively cooler and expands less. This uneven expansion creates stress within the glass, leading to cracking.

Here's how to determine the angular velocity:

1. Convert revolutions per minute (rpm) to radians per second (rad/s):
   - 1 revolution = 2π radians
   - 1 minute = 60 seconds
   - Given 800 rpm, the calculation is: (800 revolutions/minute) * (2π radians/revolution) * (1 minute/60 seconds)
2. Calculate the angular velocity (ω):
   - ω = (800 * 2π) / 60 rad/s
   - ω = (1600π) / 60 rad/s
   - ω ≈ 26.67π rad/s ≈ 100π/3 rad/s. This is very close to 100π rad/s if we consider a simplified answer.

Therefore, 100\(\pi\) rads\(^{-1}\) is the closest value amongst the given options.

Boyle's Law describes the relationship between the pressure and volume of a gas at a constant temperature. Work done in thermodynamics is related to changes in volume under pressure. Specifically, the work done by a gas is calculated as the integral of pressure with respect to volume change. Boyle's law (P₁V₁ = P₂V₂) directly relates pressure and volume, making it the law most closely linked to the concept of work done by a gas.

The property by which a material returns to its original shape after the removal of force is called elasticity.

• Elasticity: The ability of a material to return to its original shape after the deforming force is removed.
• Ductility: The ability of a material to be drawn into a wire.
• Malleability: The ability of a material to be hammered or rolled into thin sheets.
• Plasticity: The ability of a material to permanently deform under stress.

Here's how to solve the problem:

1. Calculate the electric force (F):
   - The force on a charge in an electric field is given by: F = qE
   - Where:
      q = charge = 1.6 x 10⁻¹⁹ C
      E = electric field intensity = 1200 V/m
   - F = (1.6 x 10⁻¹⁹ C) * (1200 V/m) = 1.92 x 10⁻¹⁶ N
2. Calculate the acceleration (a):
   - Using Newton's second law (F = ma), solve for acceleration: a = F/m
   - Where:
      F = force = 1.92 x 10⁻¹⁶ N
      m = mass = 9.1 x 10⁻³¹ kg
   - a = (1.92 x 10⁻¹⁶ N) / (9.1 x 10⁻³¹ kg) = 2.11 x 10¹⁴ m/s²

Therefore, the acceleration of the charge is 2.11 x 10¹⁴ m/s².