WAEC SSCE - Physics - 2013 (Objective)

The general equation of a progressive transverse wave is given by: y = A sin (kx - ωt) where A is the amplitude, k is the wave number, x is the position of the particle, ω is the angular frequency, and t is the time. Comparing this equation with the given equation, we have: A = 2 cm k = 2π/30 cm^(-1) = π/15 cm^(-1) ω = 2π/T, where T is the period Thus, we have: ω = 2π/T = 2π/(0.01 s) Substituting the value of ω, we get: 2π/(0.01 s) = π/15 cm^(-1) Simplifying this equation, we get: T = 0.01 s Therefore, the period of the wave is 0.01 s.

The electric field intensity (E) is defined as the force per unit charge. Therefore, we can find E by dividing the force (F) by the charge (q). E = F/q Substituting the given values, we have: E = 80N / (2.0 x 10\(^{-5}\) C) E = 4.0 x 10\(^6\) NC\(^{-1}\) Therefore, the magnitude of the electric field intensity is 4.0 x 10\(^6\) NC\(^{-1}\). So, the correct option is (B) 4.0 x 10⁶ NC^-1.

The correct statement is (i and ii only). The magnitude of expansion or contraction of a substance depends on the temperature change and the nature of the substance. The size of the substance does not affect the magnitude of the expansion or contraction. When a substance is heated, its temperature increases, and the particles in the substance gain kinetic energy, leading to an increase in the space between the particles. This increase in space between the particles results in expansion of the substance. The nature of the substance also plays a role in determining the magnitude of expansion or contraction. Different substances have different coefficients of thermal expansion, which is a measure of how much a substance expands or contracts when its temperature changes. Some substances expand more than others when they are heated and contract more than others when they are cooled.

The phenomenon that supports the theory that waves have a particle nature is the "photoelectric effect." This effect demonstrates that light behaves as a stream of particles, called photons, which transfer their energy to electrons in a metal surface. When the energy of a photon exceeds a certain threshold value, an electron is ejected from the metal surface. This effect cannot be explained by wave theory alone, but it can be explained by assuming that light has a particle nature. Therefore, the photoelectric effect provides strong evidence for the wave-particle duality of light.

The instrument used to determine the accurate value of the electromotive force (emf) of a cell is called a potentiometer. A potentiometer measures the potential difference across a known length of a uniform wire and compares it with the potential difference across the unknown emf source, which is connected in parallel with the wire. By adjusting the length of the wire until the potential difference across the known length is equal to the potential difference across the cell, the emf of the cell can be determined accurately. Therefore, the correct option is a potentiometer.

Images formed by a convex mirror are always behind the mirror, real, and upright. However, the images are always smaller than the actual object. This is due to the fact that convex mirrors cause light rays to diverge, making the image appear farther away and smaller than it actually is. Therefore, the correct option in this case would be "behind the mirror".

To determine the potential energy of the body at the maximum height of its motion, we need to follow these steps:

1. Calculate the speed of projection (initial velocity): From the previous solution, we determined that the speed of projection $uu$ is 6 m/s.

2. Determine the maximum height: Use the kinematic equation for the vertical motion to find the maximum height:

   $v^2=u^2-2ghv^2\; =\; u^2\; -\; 2gh$

   At the maximum height, the final velocity $vv$ is 0, so:

   $0=u^2-2gh⟹h=\frac{u^2}{2g}0\; =\; u^2\; -\; 2gh\; \backslash implies\; h\; =\; \backslash frac\{u^2\}\{2g\}$

   Substituting $u=6\text{ m/s}u\; =\; 6\; \backslash text\{\; m/s\}$ and $g=10{\text{ m/s}}^{2}g\; =\; 10\; \backslash text\{\; m/s\}^2$:

   $h=\frac{(6\text{ m/s}{)}^2}{2\times 10{\text{ m/s}}^2}=\frac{36{\text{ m}}^2\mathrm{/}{\text{s}}^2}{20{\text{ m/s}}^2}=1.8\text{ m}h\; =\; \backslash frac\{(6\; \backslash text\{\; m/s\})^2\}\{2\; \backslash times\; 10\; \backslash text\{\; m/s\}^2\}\; =\; \backslash frac\{36\; \backslash text\{\; m\}^2/\backslash text\{s\}^2\}\{20\; \backslash text\{\; m/s\}^2\}\; =\; 1.8\; \backslash text\{\; m\}$

3. Calculate the potential energy (PE): The potential energy at the maximum height is given by:

   $\text{PE}=mgh\backslash text\{PE\}\; =\; mgh$

   Convert the mass from grams to kilograms:

   $m=20\text{ g}=0.02\text{ kg}m\; =\; 20\; \backslash text\{\; g\}\; =\; 0.02\; \backslash text\{\; kg\}$

   Now substitute $m=0.02\text{ kg}m\; =\; 0.02\; \backslash text\{\; kg\}$, $g=10{\text{ m/s}}^{2}g\; =\; 10\; \backslash text\{\; m/s\}^2$, and $h=1.8\text{ m}h\; =\; 1.8\; \backslash text\{\; m\}$:

   $\text{PE}=0.02\text{ kg}\times 10{\text{ m/s}}^2\times 1.8\text{ m}=0.36\text{ J}\backslash text\{PE\}\; =\; 0.02\; \backslash text\{\; kg\}\; \backslash times\; 10\; \backslash text\{\; m/s\}^2\; \backslash times\; 1.8\; \backslash text\{\; m\}\; =\; 0.36\; \backslash text\{\; J\}$

Therefore, the potential energy of the body at the maximum height of its motion is $\boxed{{\displaystyle 0.36\text{ J}}}\backslash boxed\{0.36\; \backslash text\{\; J\}\}$

The type of thermometer used for the calibration of other thermometers is the constant volume gas thermometer. This thermometer operates on the principle of the ideal gas law, which states that the pressure and volume of a gas are proportional to its absolute temperature. In a constant volume gas thermometer, a gas is trapped in a container with a fixed volume, and its pressure is measured at different temperatures to obtain a calibration curve. This curve can then be used to calibrate other types of thermometers, such as liquid-in-glass thermometers or thermocouples. Therefore, the correct answer is constant volume gas thermometer.

The minimum energy required to cause photoelectric emission when the surface of a metal is irradiated with electromagnetic radiation of suitable frequency is called the work function. It is the amount of energy required to remove an electron from the metal surface, overcoming the attractive forces holding the electron in the metal. The energy of the incident photon must be greater than or equal to the work function for photoelectric emission to occur. If the energy of the incident photon is less than the work function, no electrons will be emitted.

The frequency of a note produced by a string under tension is directly proportional to the square root of the tension. This relationship is given by the equation: f = (1/2L) √(T/μ) Where f is the frequency, T is the tension, L is the length of the string and μ is the linear mass density of the string. Since the length and mass density of the string are constant, we can say that the frequency is directly proportional to the square root of the tension: f ∝ √T So, if we quadruple the tension, the frequency will double. Therefore, the frequency produced by the string when the tension is quadrupled will be: f' = 2f = 2 × 14Hz = 28Hz Therefore, the correct answer is 28Hz.

The slope of a linear distance-time graph represents the object's speed or rate of change of distance with respect to time. In other words, the slope is a measure of how fast the object is moving. A steeper slope indicates a faster speed, while a shallower slope indicates a slower speed. Therefore, the correct answer is speed.

The correct statement about pressure in a liquid is "the pressure in a liquid increases with depth." This means that as the depth of a liquid increases, the pressure at that point also increases. This is because the weight of the liquid above a certain depth creates a force that increases the pressure at that depth. The higher the density of a liquid, the higher the pressure it exerts, which means that the second statement is incorrect. The third statement is also incorrect because pressure in a liquid acts in all directions, not just perpendicular to the sides of the containing vessel. Finally, the fourth statement is also incorrect because pressure in a liquid is affected by the acceleration due to gravity, as the weight of the liquid above a certain depth creates a force that increases the pressure at that depth.

The statement that radioisotopes are used to induce mutations in plants and animals to obtain new and improved varieties is not correct. Radioisotopes are unstable isotopes of an element that emit radiation as they undergo decay, and they have several applications in various fields. However, inducing mutations in plants and animals is not one of them. Instead, mutagenic agents like chemicals or radiation are used for this purpose. Radioisotopes are used to trace the paths of metabolic processes in plants and animals, estimate the age of rocks, locate broken bones, and several other applications in fields such as medicine, agriculture, and industry.

To determine the speed of projection of a body projected vertically upwards in a vacuum, we can use the principles of kinematics and the given information. Here are the steps:

1. Understand the total time of flight: The total time taken for the body to go up and come back down is 1.2 seconds.

2. Determine the time to reach the maximum height: Since the time to go up is equal to the time to come down, the time to reach the maximum height is half of the total time of flight.

   $t_{\text{up}}=\frac{1.2\text{ s}}{2}=0.6\text{ s}t\_\{\backslash text\{up\}\}\; =\; \backslash frac\{1.2\; \backslash text\{\; s\}\}\{2\}\; =\; 0.6\; \backslash text\{\; s\}$

3. Use the kinematic equation for velocity: The velocity at the maximum height is 0 (since the body momentarily stops before falling back down). We can use the equation:

   $v=u-gtv\; =\; u\; -\; gt$

   where $vv$ is the final velocity (0 m/s at the maximum height), $uu$ is the initial velocity (speed of projection), $gg$ is the acceleration due to gravity (10 m/s²), and $tt$ is the time taken to reach the maximum height (0.6 s).

   Setting $v=0v\; =\; 0$:

   $0=u-g\cdot t0\; =\; u\; -\; g\; \backslash cdot\; t$

4. Solve for $uu$:

   $u=g\cdot t=10{\text{ m/s}}^2\cdot 0.6\text{ s}=6\text{ m/s}u\; =\; g\; \backslash cdot\; t\; =\; 10\; \backslash text\{\; m/s\}^2\; \backslash cdot\; 0.6\; \backslash text\{\; s\}\; =\; 6\; \backslash text\{\; m/s\}$

Therefore, the speed of projection is $\boxed{{\displaystyle 6.0\text{ m/s}}}\backslash boxed\{6.0\; \backslash text\{\; m/s\}\}$6.0 m/s

Radio waves have frequencies lower than infrared radiation. Radio waves have the lowest frequency among all the electromagnetic radiations, ranging from a few hertz to several gigahertz. On the other hand, infrared radiation has a frequency range of about 430 THz to 300 GHz. Therefore, radio waves have a lower frequency than infrared radiation.

The velocity ratio of an inclined plane is a measure of the effectiveness of the plane in reducing the force required to move an object to a certain height. It is defined as the ratio of the distance moved by the load to the distance moved by the effort. The velocity ratio of an inclined plane is dependent on the angle of inclination. As the angle of inclination increases, the velocity ratio also increases. This means that a steeper inclined plane is more effective at reducing the force required to move an object to a certain height. Therefore, the correct option is: increases with increase in the angle of inclination.

In a neutral atom, the number of positively charged protons in the nucleus is equal to the number of negatively charged electrons surrounding the nucleus. The nucleons in an atom refer to the particles present in the nucleus, which are protons and neutrons. Therefore, the correct answer is (a) protons and neutrons.

When salt is dissolved in water, it lowers the freezing point of the water. This is because adding salt lowers the temperature at which water freezes, a process known as freezing point depression. When salt is added to water, it lowers the freezing point of the water because the salt ions interfere with the formation of ice crystals. The result is that the saltwater mixture will remain in a liquid state at a lower temperature than pure water would. Therefore, the correct option is "decreases".

The rising of a liquid in an open and ended glass tube of narrow bore is called capillarity. Capillarity is the result of the combination of adhesive and cohesive forces between the liquid molecules and the molecules of the tube material. In a narrow tube, the adhesive forces between the liquid and the tube are stronger than the cohesive forces between the liquid molecules themselves, causing the liquid to rise in the tube. The narrower the tube, the higher the liquid rises due to capillary action.

The heat gained by the water can be calculated using the formula: Heat = Power × Time where Power = Current × Voltage and Time = 2 minutes = 120 seconds The voltage can be calculated using Ohm's law: Voltage = Current × Resistance Substituting the values given: Voltage = 4.0A × 50\(\Omega\) = 200V Therefore, Power = 4.0A × 200V = 800W Substituting the values in the formula: Heat = Power × Time = 800W × 120s = 96,000J Therefore, the heat gained by the water is 96,000J. The correct option is (d) 96,000J.

To calculate the acceleration of the block, we need to apply Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. Mathematically, this is expressed as a = F_net/m, where a is the acceleration, F_net is the net force, and m is the mass of the object. In this problem, the net force acting on the block is the difference between the applied force and the frictional force, i.e., F_net = F_applied - F_friction = 40N - 12N = 28N. Therefore, the acceleration of the block is a = F_net/m = 28N/5kg = 5.6ms^-2. Therefore, the correct option is 5.6ms^-2.

The maximum displacement on either side of the equilibrium position of an object in simple harmonic motion represents its **amplitude**. In simple harmonic motion, the object oscillates back and forth around a central point, which is its equilibrium position. The amplitude is the maximum displacement of the object from this equilibrium position, in either direction. It represents the "strength" or "size" of the oscillation. The other options are not correct: the **period** is the time it takes for one complete oscillation, the **wavelength** is the distance between two adjacent points in a wave that are in phase, and the **frequency** is the number of oscillations per unit time (usually measured in Hertz).

We can use the formula for the current in an AC circuit with an inductor and a resistor: \begin{equation*} I = \frac{V}{\sqrt{R^2 + (\omega L)^2}} \end{equation*} where V is the voltage, R is the resistance, L is the inductance, and \(\omega\) is the angular frequency. We can find \(\omega\) using the formula: \begin{equation*} \omega = 2\pi f \end{equation*} where f is the frequency. Substituting the given values, we get: \begin{align*} \omega &= 2\pi \times 50\text{ Hz} \\ &= 100\pi\text{ rad/s} \end{align*} Now we can substitute all the values into the first formula: \begin{align*} I &= \frac{V}{\sqrt{R^2 + (\omega L)^2}} \\ &= \frac{240\text{ V}}{\sqrt{(4\Omega)^2 + (100\pi \text{ rad/s} \times 0.12\text{ H})^2}} \\ &\approx 6.3\text{ A} \end{align*} Therefore, the current through the coil is approximately 6.3A. Answer is correct.

When a body of mass m is released on an inclined plane at an angle θ to the horizontal, the component of its weight acting down the plane is mgsinθ. The force acting parallel to the plane that causes the body to slide down is given by F = mgsinθ. The acceleration of the body down the plane is given by a = F/m = gsinθ. In this case, m = 2kg and θ = 60°. Therefore, the acceleration of the body down the plane is given by: a = gsinθ = 10ms\(^{-2}\) x sin(60°) = 8.7ms\(^{-2}\) Therefore, the correct answer is 8.7ms\(^{-2}\).

As the pump handle is slowly pushed downwards, the volume of the pump is reduced. This means that the same amount of air inside the pump is now occupying a smaller space. Since the temperature is constant, the increase in pressure results from an increase in the frequency of collisions of air molecules with the walls of the pump. The air molecules are being compressed into a smaller volume, leading to an increase in pressure. Therefore, the correct answer is: the frequency of collision of the air molecules with the walls of the pump is increased.

When a person holds a negatively charged metal rod and stands bare-footed on the ground, the negative charges will flow to the ground through the person's body. This is because the human body is a good conductor of electricity, allowing charges to flow easily through it. When a person is standing on the ground, they are in contact with a large conductive surface (the earth), which provides a pathway for the charges to flow away from the person's body and into the ground. This process is called grounding or earthing, and it helps to prevent the buildup of static electricity on the person's body.

The critical angle is the angle of incidence at which the angle of refraction is 90 degrees. Using Snell's law, we can relate the critical angle to the refractive index. At the critical angle, the sine of the angle of refraction is 1, so we can write: sin(critical angle) = 1/n where n is the refractive index. Substituting n=1.5 gives: sin(critical angle) = 1/1.5 = 0.67 Taking the inverse sine of both sides gives: critical angle = sin^-1(0.67) = 42^o Therefore, the correct answer is 42^o.

The unit of power is the watt (W), which is defined as the rate at which work is done or energy is transferred. In terms of fundamental units, power can be expressed as the product of force and velocity, which can be further expressed as mass times acceleration times velocity. Simplifying this expression, we get the unit of power as kgm²s^-3, which is option B.

The correct option is: "the final image is inverted". This statement is incorrect. The Galilean telescope consists of a converging lens (the objective lens) and a diverging lens (the eyepiece) placed at a distance equal to the sum of their focal lengths. The objective lens produces a real and inverted image of the object being observed, which is then magnified and made upright by the eyepiece lens. So, the final image is upright. The other options are: - "it is shorter than terrestial telescope" - This statement is correct. The Galilean telescope is shorter than the terrestrial telescope, as it uses a combination of lenses to produce a magnified image rather than a long focal length objective lens. - "it has a small field of view" - This statement is generally correct. The Galilean telescope has a smaller field of view compared to the terrestrial telescope due to its design, which results in a narrow angle of view. - "the final image is erect" - This statement is correct. As mentioned earlier, the final image produced by a Galilean telescope is upright or erect.

Solid friction is in opposition to motion. When two solid surfaces are in contact, there is a force that resists the relative motion between them, known as friction. In the case of solid friction, this force acts perpendicular to the surfaces in contact and depends on the normal reaction between them, which is the force exerted by one surface on the other perpendicular to the contact area. Friction is also independent of the surface area in contact and dependent on the relative motion between the layers.

The energy required to eject an electron from a metal is given by: Kinetic energy of ejected electron = Energy of photon – Work function We can rearrange this equation to find the energy of the photon: Energy of photon = Kinetic energy of ejected electron + Work function The kinetic energy of the ejected electron is given as 3.0 eV. We can convert this to joules using the conversion factor 1 eV = 1.6 x 10^-19 J: Kinetic energy of ejected electron = 3.0 eV x 1.6 x 10^-19 J/eV = 4.8 x 10^-19 J Substituting this value and the given work function into the equation for the energy of the photon: Energy of photon = 4.8 x 10^-19 J + 2.56 x 10^-19 J = 7.36 x 10^-19 J We can use the formula E = hf to relate the energy of the photon to its frequency f: E = hf where h is Planck's constant, h = 6.6 x 10^-34 J s. Rearranging the equation gives: f = E/h Substituting the values we obtained: f = (7.36 x 10^-19 J) / (6.6 x 10^-34 J s) ≈ 1.12 x 10¹⁵ Hz Therefore, the frequency of the photon required to eject an electron with a kinetic energy of 3.0 eV from a metal with a work function of 2.56 x 10^-19 J is approximately 1.12 x 10¹⁵ Hz.