Physics

31. The minimum length of a plane mirror to see your full length image is

The minimum length of a plane mirror to see your full length image is

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one quarter of your height
one-third of your height
half of your height
equal to your height
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The minimum length of a plane mirror to see your full length image is half of your height.
This is a fundamental principle of reflection from a plane mirror. To see the full image of an object in a plane mirror, the minimum vertical extent of the mirror required is half the vertical extent of the object.

Consider a person standing in front of a mirror. Light rays from the top of their head reflect off the top part of the mirror and enter their eyes. Light rays from their feet reflect off the bottom part of the mirror and enter their eyes.
– The angle of incidence equals the angle of reflection.
– The law of reflection dictates that to see the top of your head, the top edge of the mirror must be halfway between the top of your head and your eye level.
– Similarly, to see your feet, the bottom edge of the mirror must be halfway between your feet and your eye level.
– The distance between these two points on the mirror is the minimum required length. This distance is (1/2 * distance from head to eye) + (1/2 * distance from eye to feet). Since (distance from head to eye) + (distance from eye to feet) equals the total height of the person, the required mirror length is half the person’s height.

The distance of the person from the mirror does not affect the *minimum length* required, although it does affect the *field of view*.

This principle is utilized in everyday life, for instance, when installing full-length mirrors. The mirror doesn’t need to be as tall as the person.

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32. A Kelvin thermometer and a Fahrenheit thermometer both give the same r

A Kelvin thermometer and a Fahrenheit thermometer both give the same reading for a certain sample. The corresponding Celsius temperature is about

301 °C
614 °C
276 °C
273 °C
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The corresponding Celsius temperature is about 301 °C.
We are given that a Kelvin thermometer and a Fahrenheit thermometer give the same reading for a certain sample. Let this reading be x.
So, the temperature in Kelvin (K) is x, and the temperature in Fahrenheit (F) is x.
We need to find the corresponding temperature in Celsius (C).

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The conversion formulas between these scales are:
1. Fahrenheit to Celsius: C = (F – 32) * 5/9
2. Kelvin to Celsius: C = K – 273.15 (or often approximated as C = K – 273)

Let’s use the exact conversion K = C + 273.15 and F = (9/5)C + 32.
Since K = x and F = x, we have:
x = C + 273.15 (Equation 1)
x = (9/5)C + 32 (Equation 2)

Equating the right sides of Equation 1 and Equation 2:
C + 273.15 = (9/5)C + 32

Rearrange the terms to solve for C:
273.15 – 32 = (9/5)C – C
241.15 = (9/5 – 5/5)C
241.15 = (4/5)C

C = (241.15 * 5) / 4
C = 1205.75 / 4
C = 301.4375

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Rounding to the nearest whole number or considering the options, the corresponding Celsius temperature is about 301 °C.

The question asks for “about” the Celsius temperature, indicating an approximation is acceptable. Using the approximation C = K – 273 would yield C = 301.4375 – 0.15 ≈ 301.2875, still close to 301 °C. The unusual point where Kelvin and Fahrenheit scales read the same is 301.4375 in both K and °F.

33. Which one of the following pairs of quantities has no length in their

Which one of the following pairs of quantities has no length in their dimension?

Surface tension and angular momentum
Surface tension and strain
Angular momentum and mass density
Pressure gradient and angle
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The correct answer is Surface tension and strain.
We need to find the pair of quantities whose dimensions do not include length ([L]). Let’s analyze the dimensions of each quantity:
– **Surface tension:** Defined as force per unit length. Dimension is [Force]/[Length] = [MLT⁻²]/[L] = [MT⁻²]. It has no length dimension.
– **Angular momentum:** Defined as the product of moment of inertia and angular velocity (Iω) or cross product of position and linear momentum (r x p). Dimension is [ML²] * [T⁻¹] = [ML²T⁻¹]. It has a length dimension.
– **Strain:** Defined as the ratio of change in dimension to the original dimension (e.g., change in length / original length). Dimension is [L]/[L] = [Dimensionless]. It has no length dimension.
– **Mass density:** Defined as mass per unit volume. Dimension is [M]/[L³] = [ML⁻³]. It has a length dimension.
– **Pressure gradient:** Defined as change in pressure per unit distance. Dimension is [Pressure]/[Length]. Pressure is [Force]/[Area] = [MLT⁻²]/[L²] = [ML⁻²T⁻²]. So, pressure gradient is [ML⁻²T⁻²]/[L] = [ML⁻³T⁻²]. It has a length dimension.
– **Angle:** Defined as the ratio of arc length to radius. Dimension is [L]/[L] = [Dimensionless]. It has no length dimension.

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Now let’s check the pairs:
A) Surface tension ([MT⁻²]) and angular momentum ([ML²T⁻¹]). Angular momentum has length.
B) Surface tension ([MT⁻²]) and strain ([Dimensionless]). Neither has length.
C) Angular momentum ([ML²T⁻¹]) and mass density ([ML⁻³]). Both have length.
D) Pressure gradient ([ML⁻³T⁻²]) and angle ([Dimensionless]). Pressure gradient has length.

The pair with no length dimension is Surface tension and Strain.

Understanding the dimensional formulas of common physical quantities is crucial for solving such problems. Dimensional analysis helps verify the consistency of equations and understand the fundamental nature of physical quantities.

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34. Consider the following statement : “When a body is in equilibrium, the

Consider the following statement :
“When a body is in equilibrium, the sum of the clockwise moments about any point equals the sum of the anticlockwise moments about the same point.”
Which one of the following laws is described in the above statement ?

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Law of motion
Law of moments
Law of momentum
Law of magnetism
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The statement “When a body is in equilibrium, the sum of the clockwise moments about any point equals the sum of the anticlockwise moments about the same point” is the definition of rotational equilibrium. This condition is formally known as the Law of Moments, which is part of the requirements for a body to be in complete equilibrium (the other part being translational equilibrium, i.e., zero net force).
The Law of Moments is the principle that governs rotational equilibrium.
Moment (or torque) is the tendency of a force to cause rotation around an axis or pivot point. For a body to be in complete mechanical equilibrium, both the net force and the net moment acting on it must be zero.

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35. Which of the following statements regarding temperature of an object i

Which of the following statements regarding temperature of an object in Kelvin scale is/are correct ?

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  • 1. It can be a negative, zero or positive quantity.
  • 2. It can either be a negative or a positive quantity.
  • 3. It can never be negative.
  • 4. It can be a positive definite quantity.

Select the correct answer using the code given below :

1 and 2 only
2 and 4 only
3 and 4 only
4 only
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The Kelvin scale is an absolute temperature scale. The zero point (0 K) is absolute zero, the theoretical lowest possible temperature. Temperatures on the Kelvin scale are always non-negative (greater than or equal to zero).
Statement 1: Incorrect, as Kelvin temperature cannot be negative.
Statement 2: Incorrect, as Kelvin temperature cannot be negative and can be zero.
Statement 3: Correct, Kelvin temperature can never be negative (it is always $\ge 0$).
Statement 4: Interpreting “positive definite quantity” in this context to mean a quantity that is positive or zero (non-negative), this statement is correct, as Kelvin temperature is always $\ge 0$. If interpreted strictly as strictly positive (> 0), it would be incorrect as 0 K is possible. Given the options, the non-negative interpretation is most likely intended for statement 4, making both 3 and 4 correct.
Temperature on the Kelvin scale is always non-negative ($\ge 0$).
Absolute zero (0 K or -273.15 °C) is the point at which particles have minimum possible motion (though not zero motion according to quantum mechanics). The Kelvin scale is used extensively in scientific applications.

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36. Which one of the following statements about the Principle of Calorimet

Which one of the following statements about the Principle of Calorimetry is correct ?

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It is always valid.
It is valid when temperature is constant.
It is valid only when there is no change of state.
It is valid only under equilibrium condition.
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The Principle of Calorimetry is based on the law of conservation of energy. It states that in an isolated system, the total amount of heat lost by the hot bodies is equal to the total amount of heat gained by the cold bodies. This principle is fundamentally valid whenever heat exchange occurs in an isolated system, including processes involving changes of state (by accounting for latent heat) and processes involving temperature changes. Options B, C, and D state conditions under which the principle is *only* valid, which are incorrect limitations. The principle is valid even when temperature is not constant (during temperature change), when there is a change of state (by including latent heat), and it describes the process of heat exchange *towards* equilibrium, not only at equilibrium. Therefore, “It is always valid” (interpreted as valid in an isolated system for which it is defined) is the most accurate statement among the choices, as the other options describe false limitations.
The Principle of Calorimetry is based on energy conservation in thermal interactions and applies in isolated systems, irrespective of whether temperature changes or phase changes occur.
In practical calorimetry experiments, efforts are made to create an isolated system to minimize heat exchange with the surroundings and ensure the principle holds true for the components within the calorimeter.

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37. Which one of the following determines the direction of induced current

Which one of the following determines the direction of induced current ?

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Fleming's left hand rule
Fleming's right hand rule
Feynman's left hand rule
Right hand thumb rule
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Fleming’s Right-Hand Rule is used to determine the direction of the induced electric current in a conductor when it is moved in a magnetic field or when the magnetic field around it changes. The thumb, forefinger, and middle finger are held mutually perpendicular: the thumb points in the direction of motion of the conductor, the forefinger points in the direction of the magnetic field, and the middle finger points in the direction of the induced current.
Fleming’s Right-Hand Rule determines the direction of induced current, while Fleming’s Left-Hand Rule determines the direction of force on a current-carrying conductor in a magnetic field.
The phenomenon of induced current is described by Faraday’s Law of electromagnetic induction, and its direction is governed by Lenz’s Law, which is encapsulated by Fleming’s Right-Hand Rule.

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38. Which of the following statements about a body under equilibrium is/ar

Which of the following statements about a body under equilibrium is/are correct ?

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  • 1. No forces are acting.
  • 2. A number of parallel forces may be acting.
  • 3. The law of moments must apply.

Select the correct answer using the code given below :

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1, 2 and 3
2 and 3 only
1 and 3 only
2 only
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A body is under equilibrium if the net force acting on it is zero (translational equilibrium) and the net torque acting on it is zero (rotational equilibrium).
Statement 1: “No forces are acting” is incorrect. Forces can be acting, but they must be balanced, meaning the vector sum of all forces is zero.
Statement 2: “A number of parallel forces may be acting” is correct. For example, if two equal and opposite parallel forces act on a body, they form a couple, which produces a torque. For the body to be in equilibrium, this torque must be balanced by other torques, and the net force must be zero (which these two forces satisfy). More generally, parallel forces can sum to zero net force and zero net torque.
Statement 3: “The law of moments must apply” is correct. The Law of Moments states that for rotational equilibrium, the sum of clockwise moments about any point equals the sum of anticlockwise moments about the same point. This is a necessary condition for a body to be in equilibrium.
Equilibrium requires zero net force and zero net torque. The Law of Moments describes the condition for zero net torque.
A body in equilibrium can be either at rest (static equilibrium) or moving with constant velocity (dynamic equilibrium). Both require the net force and net torque to be zero.

39. Which one among the following statements is not correct?

Which one among the following statements is not correct?

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Johannes Kepler proved that the path of each planet around the Sun is elliptical with the Sun at its focus.
The first successful attempt to establish the size of the Earth is credited to Eratosthenes.
The first Greek to profess a Sun-centred or Heliocentric Universe was Sir Isaac Newton.
The famous astronomical book Almagest was compiled by Ptolemy.
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The correct option is C) The first Greek to profess a Sun-centred or Heliocentric Universe was Sir Isaac Newton.
Statement A is correct. Johannes Kepler formulated his laws of planetary motion in the early 17th century, including the first law stating that planets orbit the Sun in elliptical paths with the Sun at one focus.
Statement B is correct. Eratosthenes of Cyrene, a Greek scholar in the 3rd century BC, is famous for making the first relatively accurate calculation of the Earth’s circumference using geometry and astronomical observations.
Statement C is incorrect. The first known Greek astronomer to propose a heliocentric model of the solar system was Aristarchus of Samos in the 3rd century BC, predating Kepler and Newton by over a thousand years. Sir Isaac Newton (1643-1727) was a British physicist and mathematician, not Greek, and his work explained *why* planetary orbits are elliptical (gravity), building upon Kepler’s descriptive laws.
Statement D is correct. The Almagest is the 2nd-century AD astronomical treatise by Claudius Ptolemy, which presented a detailed geocentric model of the universe that remained the standard view for centuries.
Aristarchus’s heliocentric model was not widely accepted in antiquity, with the geocentric model of Aristotle and later Ptolemy dominating astronomical thought until the Copernican revolution in the 16th century.

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40. Electron was discovered by

Electron was discovered by

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Michael Faraday
Joseph John Thomson
Henry Cavendish
Earnest Rutherford
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The electron was discovered by Joseph John Thomson.
J.J. Thomson discovered the electron in 1897 through his experiments with cathode ray tubes, determining that cathode rays were composed of negatively charged particles much smaller than atoms.
Michael Faraday contributed significantly to electromagnetism and electrochemistry. Henry Cavendish discovered hydrogen and determined the composition of water. Ernest Rutherford conducted the gold foil experiment leading to the discovery of the atomic nucleus and later discovered the proton.

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