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 :

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

Two identical charged particles each having a mass 10 g and charge 2.0 $$\times$$ 10^$$-$$7C 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]

Two massless springs with spring constants 2 k and 9 k, 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 :

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

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

A proton, a deutron 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 :

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.

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

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 ms^$$-$$2].

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 :

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 Jg^$$-$$1 $$^\circ$$C^$$-$$1]

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

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 :

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.

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 :

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 :

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 :

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

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 $$y = (10\cos \pi x\sin {{2\pi t} \over T})$$ cm

The amplitude of the particle at $$x = {4 \over 3}$$ cm will be ___________ cm.

In the given circuit, the value of current I_L will be ____________ mA. (When R_L = 1k$$\Omega$$)

A ray of light is incident at an angle of incidence 60$$^\circ$$ on the glass slab of refractive index $$\sqrt3$$. After refraction, the light ray emerges out from other parallel faces and lateral shift between incident ray and emergent ray is 4$$\sqrt3$$ cm. The thickness of the glass slab is __________ cm.

A circular coil of 1000 turns each with area 1m² is rotated about its vertical diameter at the rate of one revolution per second in a uniform horizontal magnetic field of 0.07T. The maximum voltage generation will be ___________ V.

A monoatomic gas performs a work of $${Q \over {4}}$$ 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.