Physics Archives

251. Which one of the following is not a conservative force ?

Which one of the following is not a conservative force ?

[amp_mcq option1=”Frictional force” option2=”Electric force” option3=”Gravitational force” option4=”Spring force” correct=”option1″]

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Frictional force is not a conservative force.

A conservative force is one for which the work done in moving an object between two points is independent of the path taken, or equivalently, the work done in moving an object around a closed loop is zero. Gravitational force, electric force, and spring force are examples of conservative forces because the work done by them depends only on the initial and final positions. Frictional force, however, is a dissipative force and the work done by friction depends on the path length; the longer the path, the more work is done against friction. Work done by friction over a closed loop is generally non-zero and negative (energy is dissipated as heat).

Forces like friction and air resistance are examples of non-conservative forces. The work done by non-conservative forces leads to a change in the mechanical energy of the system, often converting mechanical energy into other forms like heat or sound.

252. The image of an object formed by a plane mirror is

The image of an object formed by a plane mirror is

[amp_mcq option1=”erect, real and larger.” option2=”erect, virtual and same size.” option3=”inverted, virtual and same size.” option4=”inverted, real and smaller.” correct=”option2″]

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The image of an object formed by a plane mirror is erect, virtual and the same size as the object.

A plane mirror forms an image that is always virtual (cannot be projected onto a screen), erect (same orientation as the object), laterally inverted (left appears right and vice versa), and of the same size as the object. The image is also located as far behind the mirror as the object is in front.

Real images are formed when light rays converge at a point after reflection or refraction, whereas virtual images are formed when light rays appear to diverge from a point. Plane mirrors produce virtual images because the reflected rays do not actually meet but only appear to meet behind the mirror.

253. When a light beam falls on a triangular glass prism, a band of colours

When a light beam falls on a triangular glass prism, a band of colours is obtained. Which one of the following statements is correct in this regard?

[amp_mcq option1=”Red light bends the most, as the refractive index of glass for red light is greatest.” option2=”Red light bends the most, as the refractive index of glass for red light is lowest.” option3=”Violet light bends the most, as the refractive index of glass for violet light is greatest.” option4=”Violet light bends the most, as the refractive index of glass for violet light is lowest.” correct=”option3″]

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The correct answer is that Violet light bends the most because the refractive index of glass for violet light is greatest.

When white light passes through a prism, it splits into its constituent colours due to dispersion. The amount of bending (deviation) of light by a prism depends on the refractive index of the prism material for that specific colour. According to Cauchy’s formula and experimental observations, the refractive index of a material decreases as the wavelength of light increases. Violet light has the shortest wavelength among the visible colours, while red light has the longest wavelength. Therefore, the refractive index of glass is highest for violet light and lowest for red light. A higher refractive index leads to a greater deviation (bending).

The deviation of light by a prism is given approximately by $\delta = (\mu – 1)A$, where $\mu$ is the refractive index of the prism material and A is the angle of the prism. Since $\mu_{\text{violet}} > \mu_{\text{red}}$, it follows that $\delta_{\text{violet}} > \delta_{\text{red}}$. This causes violet light to be deviated the most and red light the least, resulting in the separation of colours observed as a spectrum.

254. Which one of the following figures correctly shows the path of a ray o

Which one of the following figures correctly shows the path of a ray of light through a glass prism ?

[amp_mcq option1=”Image of path of light through prism” option2=”Image of path of light through prism” option3=”Image of path of light through prism” option4=”Image of path of light through prism” correct=”option1″]

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Assuming Option A depicts the standard correct path of a ray of light through a glass prism. A ray of light entering a prism from air bends towards the normal upon entering the glass (denser medium). Inside the prism, it travels in a straight line. Upon exiting the prism from glass back into air (rarer medium), it bends away from the normal.

According to Snell’s Law, when light travels from a rarer medium (like air) to a denser medium (like glass), the ray bends towards the normal. When it travels from a denser medium to a rarer medium, it bends away from the normal. For a prism, the incident ray bends towards the normal at the first surface and the emergent ray bends away from the normal at the second surface. The net deviation of the ray is always towards the base of the prism for a ray entering one face and exiting another.

Different paths might be depicted in the options, such as bending away from the normal upon entry, no bending, total internal reflection, or bending towards the apex. Only one diagram correctly shows the path based on the principles of refraction. Without seeing the specific diagrams, it is assumed option A represents the correct standard path with deviation towards the base.

255. The unit of the ratio between thrust and impulse is same as that of

The unit of the ratio between thrust and impulse is same as that of

[amp_mcq option1=”frequency” option2=”speed” option3=”wavelength” option4=”acceleration” correct=”option1″]

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The correct option is A. We need to find the unit of the ratio between thrust and impulse and compare it with the units of the given options.

Thrust is a force. The SI unit of force is Newton (N), which is equivalent to $\text{kg} \cdot \text{m/s}^2$.
Impulse is the change in momentum, or force multiplied by time. The SI unit of impulse is N·s, which is equivalent to $(\text{kg} \cdot \text{m/s}^2) \cdot \text{s} = \text{kg} \cdot \text{m/s}$.
The ratio $\frac{\text{Thrust}}{\text{Impulse}}$ has units $\frac{\text{N}}{\text{N} \cdot \text{s}} = \frac{1}{\text{s}}$.
The unit $1/\text{s}$ is the unit of frequency. Frequency is the number of cycles or events per unit time, measured in Hertz (Hz), where 1 Hz = $1/\text{s}$.
Let’s check the units of the options:
A) Frequency: $1/\text{s}$ or Hz.
B) Speed: m/s.
C) Wavelength: m.
D) Acceleration: m/s².
The unit of the ratio is the same as the unit of frequency.

Impulse is also equal to the change in momentum ($\Delta p = m \Delta v$). So the unit of impulse is also $(\text{kg}) \cdot (\text{m/s}) = \text{kg} \cdot \text{m/s}$. Using this, the ratio unit is $\frac{\text{kg} \cdot \text{m/s}^2}{\text{kg} \cdot \text{m/s}} = \frac{1}{\text{s}}$.

256. An object of mass 2000 g possesses 100 J kinetic energy. The object mu

An object of mass 2000 g possesses 100 J kinetic energy. The object must be moving with a speed of

[amp_mcq option1=”10.0 m/s” option2=”11.1 m/s” option3=”11.2 m/s” option4=”12.1 m/s” correct=”option1″]

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The correct option is A. The kinetic energy (KE) of an object is given by the formula $\text{KE} = \frac{1}{2}mv^2$, where $m$ is the mass and $v$ is the speed. Given $\text{KE} = 100 \, \text{J}$ and $m = 2000 \, \text{g} = 2 \, \text{kg}$, we can solve for $v$.

Substitute the given values into the kinetic energy formula: $100 \, \text{J} = \frac{1}{2} \times (2 \, \text{kg}) \times v^2$. This simplifies to $100 = 1 \times v^2$, so $v^2 = 100$. Taking the square root of both sides gives $v = 10 \, \text{m/s}$ (since speed is a magnitude and must be non-negative).

It is important to ensure that all units are in the standard SI system before calculation. Mass is given in grams and must be converted to kilograms (1 kg = 1000 g). Energy is given in Joules, which is the standard SI unit.

257. A tennis ball is thrown in the vertically upward direction and the bal

A tennis ball is thrown in the vertically upward direction and the ball attains a maximum height of 20 m. The ball was thrown approximately with an upward velocity of

[amp_mcq option1=”8 m/s” option2=”12 m/s” option3=”16 m/s” option4=”20 m/s” correct=”option4″]

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The correct option is D. Using the kinematic equation $v^2 = u^2 + 2as$, where $v$ is the final velocity (0 m/s at max height), $u$ is the initial velocity, $a$ is the acceleration due to gravity (-g), and $s$ is the height (20 m).

At the maximum height of a vertically thrown object, its instantaneous velocity is zero. The acceleration acting on the object throughout its flight (ignoring air resistance) is the constant acceleration due to gravity, acting downwards. Taking the upward direction as positive, $a = -g$. Using $g \approx 10 \, \text{m/s}^2$ for approximation: $0^2 = u^2 + 2(-10)(20) \implies 0 = u^2 – 400 \implies u^2 = 400 \implies u = 20 \, \text{m/s}$. Using $g \approx 9.8 \, \text{m/s}^2$: $0^2 = u^2 + 2(-9.8)(20) \implies 0 = u^2 – 392 \implies u^2 = 392 \implies u \approx 19.8 \, \text{m/s}$. Both approximations are closest to 20 m/s among the given options.

This is a standard problem in projectile motion under constant acceleration (gravity). The time taken to reach the maximum height can be found using $v = u + at$. The total time of flight is twice the time to reach the maximum height (assuming it lands at the same level).

258. Which among the following is true for propagation of sound waves ?

Which among the following is true for propagation of sound waves ?

[amp_mcq option1=”Sound can travel in vacuum and it is a transverse wave in air.” option2=”Sound cannot travel in vacuum and it is a longitudinal wave in air.” option3=”Sound can travel in vacuum and it is a longitudinal wave in air.” option4=”Sound cannot travel in vacuum and it is a transverse wave in air.” correct=”option2″]

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The correct option is B. Sound waves are mechanical waves that require a medium to propagate and cannot travel through a vacuum. In air, sound waves are longitudinal waves, meaning the particles of the medium vibrate parallel to the direction of wave propagation.

Sound transmission involves the vibration of particles in a medium. In air, this vibration creates regions of compression and rarefaction that travel through the air as a wave. Because the particle displacement is along the direction of energy propagation, it is a longitudinal wave. Vacuum lacks the particles needed to transmit these vibrations, hence sound cannot travel in a vacuum.

Examples of longitudinal waves include sound waves in fluids and solids, and seismic P-waves. Examples of transverse waves include light waves, waves on the surface of water, and seismic S-waves (in solids). Transverse waves involve particle vibration perpendicular to the direction of wave propagation.

259. Reverberation is a phenomenon associated with a

Reverberation is a phenomenon associated with a

[amp_mcq option1=”multiple refraction of sound.” option2=”multiple reflection of sound.” option3=”single refraction of sound.” option4=”single reflection of sound.” correct=”option2″]

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The correct option is B. Reverberation is the persistence of sound in an enclosed space after the sound source has stopped, caused by multiple reflections of sound waves from surfaces within the space.

Reverberation is distinct from a single echo, which is a clearly discernible reflection. Reverberation occurs when reflected sound waves arrive at the listener in rapid succession, blending together and prolonging the original sound. It is a phenomenon resulting from numerous reflections.

Refraction of sound is the bending of sound waves as they pass from one medium to another or through a medium with varying properties (like temperature or density gradients). Single reflection is responsible for echoes or contributes to the overall sound experience in a space. Reverberation time is a key parameter in architectural acoustics, describing how long it takes for sound intensity to decay by 60 dB after the source stops.

260. Nuclear energy is generated by

Nuclear energy is generated by

[amp_mcq option1=”nuclear fission and its expression was proposed by Einstein.” option2=”nuclear fission and its expression was proposed by Rutherford.” option3=”nuclear fusion and its expression was proposed by Bohr.” option4=”nuclear fusion and its expression was proposed by Heisenberg.” correct=”option1″]

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The correct option is A. Nuclear energy is typically generated through nuclear fission in power plants, and the fundamental principle linking mass and energy, which is the basis of energy release in both fission and fusion, is expressed by Einstein’s famous equation E=mc².

Nuclear power plants primarily utilize nuclear fission of heavy elements like Uranium or Plutonium to produce energy. While nuclear fusion is the source of energy in stars and a potential future energy source on Earth, current commercial nuclear power is based on fission. The relationship between the mass deficit and the energy released in nuclear reactions is described by Albert Einstein’s mass-energy equivalence principle, E=mc².

Nuclear fission is a nuclear reaction in which a heavy nucleus splits into lighter nuclei, releasing a large amount of energy. Nuclear fusion is a reaction in which light nuclei combine to form a heavier nucleus, also releasing energy. Rutherford is known for the discovery of the nucleus and the planetary model of the atom (later refined). Bohr developed a model of the atom explaining atomic spectra. Heisenberg is one of the pioneers of quantum mechanics, known for the uncertainty principle.