A length-scale (I) depends on the permittivity (e) of a dielectric material,  Boltzmann constant (kB), the absolute temperature (T), the number per unit volume (n) of certain charged particles, and the charge (q) carried by each of the particles. Which of the following expression for I is dimensionally correct?

If a particle executes uniform circular motion, choose the correct statement

If \(|\vec P\times \vec Q|=|\vec P.\vec Q|\), then angle between \(\vec P\) and \(\vec Q\) will be ______________

A book is at rest on the table which exerts a normal force on the book. If this force is considered as reaction force, what is the action force according to Newton's third law?

A particle which is constrained to move along x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as F(x) = kx + ax³. Here, k and a are positive constants. For x ≥ 0, the functional form of the potential, energy U(x) of the particles

A particle is moving with a constant velocity along a line parallel to positive X-axis. The magnitude of its angular momentum with respect to the origin is

A circular disc is rolling down in an inclined plane without slipping. The percentage of rotational energy in its total energy is ______________.

The work done by the Sun’s gravitational force on the Earth is

If the temperature of the wire is increased, then the Young’s modulus will 

If there were no gravity, which of the following will not be there for a fluid?

When a uniform rod is heated, which of the following quantity of the rod will increase

The ratio \(\gamma =\frac { { C }_{ p } }{ { C }_{ V } } \) for a gas mixture consisting of 8 g of helium and 16 g of oxygen is

The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are

Two simple pendulums of time periods 2.0 s & 2.1 s are made to vibrate simultaneously. They are in phase initially, after how may vibrations are there in the same phase?

A transverse wave moves from a medium A to a medium B. In medium A, the velocity of the transverse wave is 500 ms^-1 and the wavelength is 5 m. The frequency and the wavelength of the wave in medium B when its velocity is 600 ms^-1, respectively are 

Deduce dimensional formulae of Boltzmann's constant

An object is thrown vertically downward. What is the acceleration experienced by the object?

Can a single isolated force exist in nature? Explain your answer

Define the different types of potential energy?

When a tree is cut, the cut is made on the side facing the direction in which the tree is required to fall. Why?

Define stress and strain.

State the second law of thermodynamics in terms of entropy.

Write down the equation of time period for linear harmonic oscillator.

What is Reverberation?

In a physical units, how many units are there in 1 metre?
1 micron (\(\mu\)) = 10^-6 m
Given data:
1 AU = 1.496\(\times\)10¹¹m
1 ly = 9.467\(\times\)10¹⁵m
1 mm = 10^-6m
1 parsec = 3.08\(\times\)10¹⁶m

The following graphs represent position-time graphs. Arrange the graphs in ascending order of increasing speed.

Define one newton.

What is the stopping distance for a vehicle, of mass m moving with speed v along a level road, if the co-efficient of friction between the tyres and the road is \(\mu\)?

A metre stick is balanced on a knife edge at its centre. When two coins, each of mass 5g are put one on top of the other at the 12.0 cm mark, the stick is found to be balanced at 45.0 cm, what is the mass of the meter stick?

A particle is projected upward from the surface of the earth (radius) with a K.E equal to half the minimum value needed for it to escape. To which height, does it rise above the surface of earth?

Write the main features of the prevost theory.

State and explain Boyle's law.

Calculate the speed of sound in a steel rod whose Young’s modulus Y = 2\(\times\)10¹¹ N m^-2 and \(\rho\) = 7800 kg m^-3.