Physics

61. Which one of the following is the audible range of hearing for humans

Which one of the following is the audible range of hearing for humans ?

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20 kHz – 200 kHz
20 Hz – 20 kHz
20 Hz – 35 kHz
20 Hz – 40 kHz
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The correct option is B. The generally accepted audible range of hearing for young, healthy humans is from 20 Hz to 20 kHz.
– ‘Hz’ stands for Hertz, which is a unit of frequency (cycles per second).
– ‘kHz’ stands for kilohertz, which is 1000 Hertz.
– The lower limit of human hearing is around 20 Hz, and the upper limit is around 20,000 Hz (20 kHz).
Hearing range can vary between individuals and typically decreases with age, especially at higher frequencies. Frequencies below 20 Hz are called infrasound, and frequencies above 20 kHz are called ultrasound. Humans cannot hear these sounds, although some animals can.

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62. Which one among the following does NOT have any linkage with the pheno

Which one among the following does NOT have any linkage with the phenomenon of electromagnetic induction ?

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Electric transformer
Induction cooker
Galvanometer
Electron microscope
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Electromagnetic induction is the phenomenon where a change in magnetic flux through a circuit induces an electromotive force (EMF) or voltage, which can drive a current. This is described by Faraday’s Law of Induction. An electric transformer works entirely on the principle of mutual induction between coils. An induction cooker heats a metal pan by inducing eddy currents within it using a changing magnetic field, which is a direct application of electromagnetic induction. A galvanometer is a device used to detect and measure electric current. Its operation is typically based on the motor principle: a current-carrying coil placed in a magnetic field experiences a torque, causing it to deflect. This principle is derived from the Lorentz force on moving charges in a magnetic field, and while related to electromagnetism, it is distinct from electromagnetic *induction* (generating voltage/current from changing magnetic fields). An electron microscope uses magnetic lenses to focus beams of electrons. This focusing action is achieved by the Lorentz force exerted by magnetic fields on the moving electrons, not electromagnetic induction. However, considering the options, the galvanometer’s operating principle (motor effect) is most clearly and fundamentally distinct from electromagnetic induction, which is the basis of the transformer and induction cooker. The electron microscope uses magnetic fields to steer charges, a direct application of Lorentz force. Out of C and D, C (Galvanometer) is the most conventional example of a device whose core principle is the motor effect rather than induction.
Electromagnetic induction is the process of generating voltage/current through changing magnetic fields (Faraday’s Law). The motor principle (force on a current in a magnetic field) and the Lorentz force (force on a moving charge in a magnetic field) are related but distinct principles of electromagnetism. Transformers and induction cookers directly rely on electromagnetic induction. A galvanometer primarily relies on the motor principle.
The relationship between the motor principle and electromagnetic induction is linked by Lenz’s Law and energy conservation. However, the fundamental operational principle of a galvanometer is the torque on a current loop, not the generation of current by changing flux.

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63. Which one of the following heat transfer mechanism does NOT require a

Which one of the following heat transfer mechanism does NOT require a medium ?

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Conduction
Convection
Radiation
Collision
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Heat transfer occurs through three primary mechanisms: conduction, convection, and radiation. Conduction is the transfer of heat through direct contact and molecular vibrations within a material; it requires a medium (solid, liquid, or gas). Convection is the transfer of heat through the bulk movement of a fluid (liquid or gas); it requires a medium that can flow. Radiation is the transfer of heat through electromagnetic waves, such as infrared radiation. These waves can travel through a vacuum (like space) and do not require a physical medium to transfer energy. Collision is not a distinct primary heat transfer mechanism; energy transfer through molecular collisions is the basis of conduction and part of convection at the molecular level. Therefore, radiation is the only mechanism listed that does not require a medium.
Conduction and convection require a medium for heat transfer, while radiation does not. Heat from the Sun reaches Earth through radiation across the vacuum of space.
Examples: Conduction heats the handle of a metal spoon in hot soup. Convection heats water in a pot as warmer water rises and cooler water sinks. Radiation is felt as warmth from a fire or the sun. All three mechanisms can occur simultaneously in many situations, but one often dominates depending on the conditions.

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64. A canon shoots a ball upwards with an initial speed of 100 m/s. The to

A canon shoots a ball upwards with an initial speed of 100 m/s. The total time of flight of the ball is 20 s before it hits the ground. The ball looses 70% of its speed after hitting the ground. Which among the following is the correct height that the ball will bounce up after its first bounce? (g=10 m/s²)

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100 m
70 m
50 m
45 m
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The ball is shot upwards with an initial speed of 100 m/s. In vertical motion under gravity (g=10 m/s²), the time taken to reach the maximum height is given by t_up = u/g = 100/10 = 10 s. The time taken to fall back to the ground from the maximum height is also 10 s. The total time of flight before the first bounce is t_up + t_down = 10 + 10 = 20 s, which matches the given information. The speed of the ball just before hitting the ground after falling from its peak height is equal to its initial projection speed, which is 100 m/s (downwards). After hitting the ground, the ball loses 70% of its speed. So, the speed after the first bounce is (100% – 70%) of 100 m/s = 30% of 100 m/s = 0.30 * 100 m/s = 30 m/s (upwards). To find the height the ball bounces up, we use the equation v² = u² + 2as, where the final velocity at the peak height is v=0, the initial velocity after bounce is u=30 m/s, and the acceleration is a=-g=-10 m/s². So, 0² = 30² + 2 * (-10) * h. This simplifies to 0 = 900 – 20h, so 20h = 900, which gives h = 900/20 = 45 meters.
Understanding projectile motion under gravity, calculating time of flight, speed before impact, calculating speed after an inelastic collision (loss of speed), and calculating the maximum height reached with a new initial velocity.
The collision with the ground is inelastic as the ball loses speed. The coefficient of restitution (e) for this bounce would be the ratio of the speed after bounce to the speed before bounce, i.e., e = 30/100 = 0.3. The maximum height reached after a bounce with speed v is given by h = v² / (2g).

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65. Which one among the following has largest energy per photon ?

Which one among the following has largest energy per photon ?

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X-ray
Ultra-violet ray
Visible-ray
Infra-red ray
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The energy of a photon is directly proportional to its frequency. In the electromagnetic spectrum, energy increases as frequency increases and wavelength decreases. Among the given options, X-rays have the highest frequency (and shortest wavelength), followed by Ultra-violet rays, Visible rays, and Infra-red rays.
– The relationship between photon energy (E), Planck’s constant (h), frequency (f), speed of light (c), and wavelength (λ) is given by E = hf = hc/λ.
– Higher frequency or shorter wavelength corresponds to higher photon energy.
– The order of electromagnetic radiation in increasing frequency (and thus increasing energy per photon) is: Radio, Microwave, Infrared, Visible, Ultraviolet, X-ray, Gamma ray.
Visible light occupies a small portion of the spectrum. Infrared is below visible light in frequency, and Ultraviolet, X-rays, and Gamma rays are above visible light in frequency. X-rays are high-energy electromagnetic radiation capable of penetrating various materials, widely used in medical imaging and security screening.

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66. In experiment #1, a bar magnet is moved towards a conducting wire loop

In experiment #1, a bar magnet is moved towards a conducting wire loop axially, with the magnet’s north pole facing the loop. In experiment #2, the same process as in experiment #1 is repeated except that the south pole of the magnet faces the loop. Which one of the following statements is true in this context?

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The direction of current in the loop will be of opposite nature in both the experiments.
The direction of current in the loop will be the same in both the experiments.
No current will flow in either of the two experiments.
More current will flow in the loop in experiment #1.
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The direction of current in the loop will be of opposite nature in both the experiments.
This question is based on Faraday’s Law of electromagnetic induction and Lenz’s Law. Faraday’s Law states that a changing magnetic flux through a loop induces an electromotive force (EMF), which drives a current in a conducting loop. Lenz’s Law provides the direction of the induced current: it flows in such a direction as to oppose the change in magnetic flux that produced it.
In experiment #1, the North pole of the bar magnet is moved towards the loop. This increases the magnetic flux through the loop in the direction of the magnet’s approaching field lines (which emerge from the North pole). To oppose this increase, the induced current in the loop creates a magnetic field pointing away from the magnet. By the right-hand rule, this corresponds to a specific direction of current flow (e.g., counter-clockwise when viewed from the magnet).
In experiment #2, the South pole of the same magnet is moved towards the loop. This increases the magnetic flux through the loop in the direction of the magnet’s approaching field lines (which enter the South pole). To oppose this increase, the induced current in the loop creates a magnetic field pointing away from the magnet’s approaching South pole (i.e., in the direction of the field lines leaving a South pole). By the right-hand rule, this corresponds to the opposite direction of current flow compared to experiment #1 (e.g., clockwise when viewed from the magnet). Therefore, the direction of the induced current will be opposite in the two experiments.
Lenz’s law is a consequence of the conservation of energy. If the induced current’s magnetic field reinforced the change in flux, the process would accelerate, producing energy indefinitely, which violates the law of conservation of energy. The strength of the induced current depends on the speed of the magnet and the strength of its magnetic field.

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67. A wire of resistance R is cut into four equal parts. These parts are t

A wire of resistance R is cut into four equal parts. These parts are then connected in parallel. If the equivalent resistance of this combination is R’, then the ratio $\frac{\text{R’}}{\text{R}}$ is :

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$ rac{1}{16}$
$ rac{1}{4}$
4
16
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The ratio $\frac{\text{R’}}{\text{R}}$ is $\frac{1}{16}$.
Let the original resistance of the wire be R. When the wire is cut into four equal parts, the resistance of each part becomes $\frac{R}{4}$ (assuming uniform material and cross-section). Let these four parts be $R_1, R_2, R_3, R_4$, where $R_1 = R_2 = R_3 = R_4 = \frac{R}{4}$. These parts are then connected in parallel. The equivalent resistance R’ of resistances connected in parallel is given by the formula: $\frac{1}{R’} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \frac{1}{R_4}$. Substituting the values, we get: $\frac{1}{R’} = \frac{1}{R/4} + \frac{1}{R/4} + \frac{1}{R/4} + \frac{1}{R/4} = \frac{4}{R} + \frac{4}{R} + \frac{4}{R} + \frac{4}{R} = \frac{4+4+4+4}{R} = \frac{16}{R}$. Therefore, $R’ = \frac{R}{16}$. The required ratio $\frac{\text{R’}}{\text{R}}$ is $\frac{R/16}{R} = \frac{1}{16}$.
The resistance of a wire is directly proportional to its length. Cutting a wire into four equal parts reduces the length of each part to one-fourth of the original length, thus reducing the resistance of each part to R/4. Connecting resistors in parallel decreases the total equivalent resistance compared to the individual resistances. This principle is used in electrical circuits to control current flow.

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68. A simple harmonic motion of a particle is represented as, y = 10 cos ω

A simple harmonic motion of a particle is represented as, y = 10 cos ωt 10. The acceleration of the particle at time t = $\frac{\pi}{2\omega}$ will be : (symbols here carry their usual meanings)

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10 ω
$-10omega^2$
0
$ rac{10}{omega}$
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The correct answer is 0.
The given equation for the simple harmonic motion of a particle is $y = 10 \cos \omega t + 10$. This represents the displacement of the particle from a reference point (in this case, an origin shifted by 10 units). The velocity of the particle is the first derivative of displacement with respect to time: $v = \frac{dy}{dt} = \frac{d}{dt}(10 \cos \omega t + 10) = -10 \omega \sin \omega t$. The acceleration of the particle is the first derivative of velocity with respect to time: $a = \frac{dv}{dt} = \frac{d}{dt}(-10 \omega \sin \omega t) = -10 \omega^2 \cos \omega t$. We need to find the acceleration at time $t = \frac{\pi}{2\omega}$. Substituting this value of $t$ into the acceleration equation: $a\left(t=\frac{\pi}{2\omega}\right) = -10 \omega^2 \cos\left(\omega \cdot \frac{\pi}{2\omega}\right) = -10 \omega^2 \cos\left(\frac{\pi}{2}\right)$. Since $\cos\left(\frac{\pi}{2}\right) = 0$, the acceleration at this time is $a = -10 \omega^2 \cdot 0 = 0$.
In simple harmonic motion described by $y = A \cos(\omega t + \phi) + C$, the term $A \cos(\omega t + \phi)$ represents the oscillation about the equilibrium position. The acceleration is proportional to the displacement from the equilibrium position and directed towards it ($a = -\omega^2 (y-C)$). In this case, the equilibrium position is at $y=10$. At $t = \frac{\pi}{2\omega}$, the displacement $y = 10 \cos(\frac{\pi}{2}) + 10 = 10(0) + 10 = 10$. Since the displacement is equal to the equilibrium position, the acceleration is zero, as expected.

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69. Which one of the following conservation laws is a consequence of the N

Which one of the following conservation laws is a consequence of the Newton’s third law of motion ?

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Conservation of energy
Conservation of momentum
Conservation of charge
Conservation of mass
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The correct answer is B. The law of conservation of momentum is a direct consequence of Newton’s third law of motion when applied to a system of particles.
– Newton’s third law states that for every action, there is an equal and opposite reaction. If object A exerts a force on object B, then object B exerts an equal and opposite force on object A.
– When considering a system of two interacting objects, the forces they exert on each other are internal forces. According to the third law, these internal forces cancel out as a pair ($\vec{F}_{\text{AB}} = -\vec{F}_{\text{BA}}$).
– Applying Newton’s second law ($\vec{F} = m\vec{a} = d\vec{p}/dt$) to the system, the total internal force is zero. Thus, the rate of change of total momentum of the system due to internal forces is zero.
– In the absence of external forces, the total momentum of the system remains constant. This is the principle of conservation of momentum.
Newton’s laws of motion are fundamental to classical mechanics. While conservation of energy, charge, and mass are also fundamental physical laws, the conservation of momentum is the one most directly and explicitly derived from Newton’s third law in the context of interactions between particles.

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70. A sound wave of frequency of 2 kHz has a wavelength of 35 cm in a give

A sound wave of frequency of 2 kHz has a wavelength of 35 cm in a given medium. How long will it take to travel a distance of 2⋅1 km through the medium ?

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30 s
2⋅1 s
3⋅0 s
4⋅1 s
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The correct answer is C. We need to calculate the time taken using the relationship between speed, distance, and time, after first determining the speed of the sound wave.
– The speed of a wave ($v$) is given by the product of its frequency ($f$) and wavelength ($\lambda$): $v = f \times \lambda$.
– Given $f = 2 \text{ kHz} = 2000 \text{ Hz}$ and $\lambda = 35 \text{ cm} = 0.35 \text{ m}$.
– Speed $v = 2000 \text{ Hz} \times 0.35 \text{ m} = 700 \text{ m/s}$.
– The time ($t$) taken to travel a distance ($d$) is given by $t = d / v$.
– Given $d = 2.1 \text{ km} = 2100 \text{ m}$.
– Time $t = 2100 \text{ m} / 700 \text{ m/s} = 3 \text{ seconds}$.
The units were carefully converted to meters and seconds before calculation to ensure consistency in the final answer. The frequency is given in kilohertz (kHz) and the wavelength in centimeters (cm), requiring conversion to standard SI units (Hz and m). The distance is given in kilometers (km), also requiring conversion to meters.

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