Identify the pair of physical quantities that have same dimensions:
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Identify the pair of physical quantities that have same dimensions:
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An object of mass $$5$$ kg is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of $$10$$ N throughout the motion. The ratio of time of ascent to the time of descent will be equal to : [Use $$g = 10$$ m s$$^{-2}$$]
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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
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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 :
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A fly wheel is accelerated uniformly from rest and rotates through $$5$$ rad in the first second. The angle rotated by the fly wheel in the next second, will be :
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The distance between Sun and Earth is $$R$$. The duration of year if the distance between Sun and Earth becomes $$3R$$ will be :
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A $$100$$ g of iron nail is hit by a $$1.5$$ kg hammer striking at a velocity of $$60$$ ms$$^{-1}$$. 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 $$= 0.42$$ J g$$^{-1}$$ °C$$^{-1}$$]
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A Carnot engine takes $$5000$$ kcal of heat from a reservoir at $$727°$$C and gives heat to a sink at $$127°$$C. The work done by the engine is
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Two massless springs with spring constants $$2k$$ and $$9k$$, carry $$50$$ g and $$100$$ 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 :
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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 :
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Two identical charged particles each having a mass $$10$$ g and charge $$2.0 \times 10^{-7}$$ 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 $$g = 10$$ ms$$^{-2}$$]
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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 :
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If the charge on a capacitor is increased by $$2C$$, the energy stored in it increases by $$44\%$$. The original charge on the capacitor is (in $$C$$)
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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?
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The soft-iron is a suitable material for making an electromagnet. This is because soft-iron has
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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 :
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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
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An electric bulb is rated as $$200$$ W. What will be the peak magnetic field at $$4$$ m distance produced by the radiations coming from this bulb? Consider this bulb as a point source with $$3.5\%$$ efficiency.
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The light of two different frequencies whose photons have energies $$3.8$$ eV and $$1.4$$ eV respectively, illuminate a metallic surface whose work function is $$0.6$$ eV successively. The ratio of maximum speeds of emitted electrons for the two frequencies respectively will be :
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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 :
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A body is projected from the ground at an angle of $$45°$$ with the horizontal. Its velocity after $$2$$ s is $$20$$ m s$$^{-1}$$. The maximum height reached by the body during its motion is ______ m. (use $$g = 10$$ m s$$^{-2}$$)
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In an experiment to verify Newton's law of cooling, a graph is plotted between the temperature difference $$(\Delta T)$$ of the water and surroundings and time as shown in figure. The initial temperature of water is taken as $$80°$$C. The value of $$t_2$$ as mentioned in the graph will be ______
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A monoatomic gas performs a work of $$\frac{Q}{4}$$ where $$Q$$ is the heat supplied to it. The molar heat capacity of the gas will be ______ $$R$$.
Where $$R$$ is the gas constant.
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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 $$y = \left(10 \cos \pi x \sin \frac{2\pi t}{T}\right)$$ cm. The amplitude of the particle at $$x = \frac{4}{3}$$ cm will be ______ cm.
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A potentiometer wire of length $$10$$ m and resistance $$20$$ $$\Omega$$ is connected in series with a $$25$$ V battery and an external resistance $$30$$ $$\Omega$$. A cell of emf $$E$$ in secondary circuit is balanced by $$250$$ cm long potentiometer wire. The value of $$E$$ (in volt) is $$\frac{x}{10}$$. The value of $$x$$ is ______.
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A circular coil of $$1000$$ turns each with area $$1$$ m$$^2$$ is rotated about its vertical diameter at the rate of one revolution per second in a uniform horizontal magnetic field of $$0.07$$ T. The maximum voltage generation will be ______ V.
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A ray of light is incident at an angle of incidence $$60°$$ 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 $$4\sqrt{3}$$ cm. The thickness of the glass slab is ______ cm.
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A sample contains $$10^{-2}$$ kg each of two substances $$A$$ and $$B$$ with half lives $$4$$ s and $$8$$ s respectively. The ratio of their atomic weights is $$1 : 2$$. The ratio of the amounts of $$A$$ and $$B$$ after $$16$$ s is $$\frac{x}{100}$$. The value of $$x$$ is ______.
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In the given circuit, the value of current $$I_L$$ will be ______ mA. (When $$R_L = 1$$ k$$\Omega$$)
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An antenna is placed in a dielectric medium of dielectric constant $$6.25$$. If the maximum size of that antenna is $$5.0$$ mm, it can radiate a signal of minimum frequency of ______ GHz.
(Given $$\mu_r = 1$$ for dielectric medium)
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