Five capacitors each of capacitance are connected as shown in the figure. The ratio of equivalent capacitance between and and the equivalent capacitance between and is
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Official Solution
Correct Option: (1)
Step 1: Observe the circuit symmetry. The five capacitors of equal capacitance form a closed pentagon. Each side of the pentagon has one capacitor.
Step 2: Equivalent capacitance between and . Between points and , there are two parallel paths: - One path consists of two capacitors in series . - The other path consists of three capacitors in series . These two paths are in parallel, so:
Step 3: Equivalent capacitance between and . Between and , the two paths are: - One capacitor directly: . - Four capacitors in series: . Hence:
Step 4: Find the ratio.
Step 5: Conclusion. The required ratio is .
02
PYQ 2020
medium
physicsID: mht-cet-
A mass suspended from a spring stretches it by when on the surface of the earth. The mass is then taken to a height of above earth’s surface and again suspended from the same spring. At this altitude the extension of the spring is (Radius of earth )
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Official Solution
Correct Option: (3)
Step 1: Relation between extension and gravity. Extension of a spring is directly proportional to the weight acting on it:
Step 2: Acceleration due to gravity at height . At a height above the earth’s surface,
Step 3: Substitute given values.
Step 4: Calculate new extension. Original extension .
Step 5: Conclusion. The extension of the spring at the given altitude is .
03
PYQ 2020
medium
physicsID: mht-cet-
In a resonance tube, the first and second resonance are heard when water level is and respectively below the open end of the tube. The inner diameter of the tube is
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Official Solution
Correct Option: (2)
Step 1: Effective length condition in resonance tube. For first resonance: For second resonance:
Step 2: Subtract the two equations.
Step 3: Substitute given values.
Step 4: Calculate end correction.
Step 5: Relation between end correction and radius.
Step 6: Find inner diameter.
Step 7: Conclusion. The inner diameter of the tube is .
04
PYQ 2020
medium
physicsID: mht-cet-
Light of frequency 2 times the threshold frequency is incident on a photo-sensitive material. If the frequency is made rd and intensity is doubled then the photocurrent will:
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be doubled
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be zero
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be rd
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be tripled
Official Solution
Correct Option: (2)
Step 1: Understanding Photoelectric Effect. The photoelectric effect depends on the frequency of the incident light. If the frequency of the light is less than the threshold frequency, no photocurrent is generated, regardless of the intensity. Since the frequency is now reduced to rd of the original value, it will be below the threshold frequency and no electrons will be ejected from the material. Hence, the photocurrent will be zero. Step 2: Final Answer. Thus, the photocurrent will be zero.
05
PYQ 2020
medium
physicsID: mht-cet-
The radiations of energies 1eV and 2.5eV are incident on a metal surface having work function 0.5 eV. The ratio of the maximum velocities of the emitted photo-electrons is:
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1:1
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1:2
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1:3
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1:4
Official Solution
Correct Option: (2)
Step 1: Kinetic Energy of Photo-electrons. The kinetic energy of a photo-electron is given by:
where is the work function of the metal. For the first radiation with energy 1 eV:
For the second radiation with energy 2.5 eV:
The maximum velocity of the emitted photo-electrons is related to the kinetic energy by:
where is the mass of the electron and is its velocity. Thus, the ratio of the velocities is:
Step 2: Final Answer. Thus, the ratio of the velocities is 1:2.
06
PYQ 2020
medium
physicsID: mht-cet-
An electron moving with initial velocity is moving in a magnetic field . Then its de-Broglie wavelength:
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increases with time
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first increases and then decreases
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decreases with time
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remains constant
Official Solution
Correct Option: (4)
Step 1: De-Broglie Wavelength Formula. The de-Broglie wavelength of a particle is given by:
where is Planck's constant and is the momentum of the electron. Since the magnetic force does not work on the electron (it only changes the direction of the velocity), the speed and hence the momentum of the electron remains constant. Therefore, the de-Broglie wavelength remains constant. Step 2: Final Answer. Thus, the de-Broglie wavelength remains constant.
07
PYQ 2025
medium
physicsID: mht-cet-
Two spherical black bodies radiate the same amount of heat per second. If their temperatures are and , and their radii are and , respectively, find the relation between their temperatures and radii.
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Official Solution
Correct Option: (1)
The problem involves two spherical black bodies radiating the same amount of heat per second. According to Stefan-Boltzmann Law, the power radiated by a spherical black body is given by:
where is the Stefan-Boltzmann constant, is the surface area, and is the temperature of the black body.
For a sphere, the surface area . Thus, the power radiated by each sphere can be given as:
Since both bodies radiate the same amount of heat per second, we equate and :
We can cancel and from both sides:
Rearranging the equation, we get:
Taking the fourth root on both sides:
Now, if we assume the relation , it implies:
Thus, .
Since both sides match, the correct relation is indeed .
