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Physics

Identify the pair of physical quantities that have same dimensions:

The distance between Sun and Earth is \( R \). The duration of year if the distance between Sun and Earth becomes \( 3R \) will be:

3.

A stone of mass \( m \), tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string is:

4.

Two identical charged particles each having a mass \( 10 \ \text{g} \) and charge \( 2.0 \times 10^{-7} \ \text{C} \) are placed on a horizontal table with a separation of \( L \) between them such that they stay in limited equilibrium. If the coefficient of friction between each particle and the table is \( 0.25 \), find the value of \( L \). [Use \( g = 10 \ \text{ms}^{-2} \)]

5.

A Carnot engine takes \( 5000 \ \text{kcal} \) of heat from a reservoir at \( 727^\circ \text{C} \) and gives heat to a sink at \( 127^\circ \text{C} \). The work done by engine is:

6.

Two massless springs with spring constants \( 2k \) and \( 9k \), carry \( 50 \ \text{g} \) and \( 100 \ \text{g} \) masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitudes will be:

7.

What will be the most suitable combination of three resistors \( A = 2\Omega \), \( B = 4\Omega \), \( C = 6\Omega \) so that \( \left(\frac{22}{3}\right)\Omega \) is equivalent resistance of combination?

8.

The soft-iron is a suitable material for making an electromagnet. This is because soft-iron has:

9.

A proton, a deuteron and an \( \alpha \)- particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is:

10.

Given below are two statements:
Statement-I: The reactance of an ac circuit is zero. It is possible that the circuit contains a capacitor and an inductor.
Statement-II: In ac circuit, the average power delivered by the source never becomes zero.
In the light of the above statements, choose the correct answer from the options given below:

11.

Potential energy as a function of \( r \) is given by \( U=\frac{A}{r^{10}}-\frac{B}{r^{5}} \), where \( r \) is the interatomic distance, \( A \) and \( B \) are positive constants. The equilibrium distance between the two atoms will be:

12.

An object of mass \( 5 \, \text{kg} \) is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of \( 10 \, \text{N} \) throughout the motion. The ratio of time of ascent to the time of descent will be equal to: [Use \( g=10 \, \text{ms}^{-2} \)].

13.

A fly wheel is accelerated uniformly from rest and rotates through \( 5 \,\text{rad} \) in the first second. The angle rotated by the fly wheel in the next second, will be:

14.

A \( 100 \,\text{g} \) of iron nail is hit by a \( 1.5 \,\text{kg} \) hammer striking at a velocity of \( 60 \,\text{m}\,\text{s}^{-1} \). What will be the rise in the temperature of the nail if one fourth of energy of the hammer goes into heating the nail? [Specific heat capacity of iron \( = 0.42 \,\text{J}\,\text{g}^{-1}\,{}^\circ\text{C}^{-1} \)]

15.

If the charge on a capacitor is increased by \( 2 \,\text{C} \), the energy stored in it increases by \( 44\% \). The original charge on the capacitor is (in \( \text{C} \)) :

16.

A long cylindrical volume contains a uniformly distributed charge of density \( \rho \). The radius of cylindrical volume is \( R \). A charge particle (\( q \)) revolves around the cylinder in a circular path. The kinetic energy of the particle is:

17.

An electric bulb is rated as \( 200 \,\text{W} \). What will be the peak magnetic field at \( 4 \,\text{m} \) distance produced by the radiations coming from this bulb? Consider this bulb as a point source with \( 3.5\% \) efficiency.

18.

The light of two different frequencies whose photons have energies \( 3.8 \,\text{eV} \) and \( 1.4 \,\text{eV} \) respectively, illuminate a metallic surface whose work function is \( 0.6 \,\text{eV} \) successively. The ratio of maximum speeds of emitted electrons for the two frequencies respectively will be:

19.

Two light beams of intensities in the ratio of \( 9:4 \) are allowed to interfere. The ratio of the intensity of maxima and minima will be:

20.

In Bohr’s atomic model of hydrogen, let \( K \), \( P \) and \( E \) are the kinetic energy, potential energy and total energy of the electron respectively. Choose the correct option when the electron undergoes transitions to a higher level:

21.

A body is projected from the ground at an angle of \( 45^\circ \) with the horizontal. Its velocity after \( 2 \, \text{s} \) is \( 20 \, \text{ms}^{-1} \). The maximum height reached by the body during its motion is _______ \( \text{m} \). (use \( g = 10 \, \text{ms}^{-2} \) )

22.

An antenna is placed in a dielectric medium of dielectric constant \( 6.25 \). If the maximum size of that antenna is \( 5.0 \, \text{mm} \), it can radiate a signal of minimum frequency of _______ \( \text{GHz} \). (Given \( \mu_1 = 1 \) for dielectric medium)

23.

A potentiometer wire of length \( 10 \, \text{m} \) and resistance \( 20 \, \Omega \) is connected in series with a \( 25 \, \text{V} \) battery and an external resistance \( 30 \, \Omega \). A cell of emf \( E \) in secondary circuit is balanced by \( 250 \, \text{cm} \) long potentiometer wire. The value of \( E \) (in volt) is \( \frac{x}{10} \). The value of \( x \) is ________.

24.

Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfere to produce a stationary wave whose equation is given by \( y=(10 \cos \pi x \sin \frac{2 \pi t}{T}) \, \text{cm} \). The amplitude of the particle at \( x=\frac{4}{3} \, \text{cm} \) will be _______ \( \text{cm} \).

25.

In the given circuit, the value of current \( I_{L} \) will be ________ \( \text{mA} \). (When \( R_{L} = 1 \, \text{k}\Omega \))

26.

A sample contains \( 10^{-2} \) \( \text{kg} \) each of two substances \( A \) and \( B \) with half lives \( 4 \, \text{s} \) and \( 8 \, \text{s} \) respectively. The ratio of their atomic weights is \( 1:2 \). The ratio of the amounts of \( A \) and \( B \) after \( 16 \, \text{s} \) is \( \dfrac{x}{100} \). The value of \( x \) is ________.

27.

A ray of light is incident at an angle of incidence \( 60^\circ \) on the glass slab of refractive index \( \sqrt{3} \). After refraction, the light ray emerges out from other parallel faces and lateral shift between incident ray and emergent ray is \( 4\sqrt{3} \, \text{cm} \). The thickness of the glass slab is ________ \( \text{cm} \).

28.

A circular coil of \( 1000 \) turns each with area \( 1 \, \text{m}^{2} \) is rotated about its vertical diameter at the rate of one revolution per second in a uniform horizontal magnetic field of \( 0.07 \, \text{T} \). The maximum voltage generation will be ________ \( \text{V} \).

29.

A monoatomic gas performs a work of \( \dfrac{Q}{4} \) where \( Q \) is the heat supplied to it. The molar heat capacity of the gas will be ________ \( R \) during this transformation. Where \( R \) is the gas constant.

30.

In an experiment to verify Newton’s law of cooling, a graph is plotted between, the temperature difference \( (\Delta T) \) of the water and surrounding and time as shown in figure. The initial temperature of water is taken as \( 80^\circ \text{C} \). The value of \( t_{2} \) as mentioned in the graph will be ________.

JEE Main 2022 24th June Evening Shift

Physics Chemistry Mathematics

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If the charge on a capacitor is increased by \( 2 \,\text{C} \), the energy stored in it increases by \( 44\% \). The original charge on the capacitor is (in \( \text{C} \)) :

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