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L, C and R represent the value of inductance, capacitance, and resistance, respectively. The factor which has the same dimensions as that of the inverse of the resonance frequency is:
A solid sphere is in rolling motion. In rolling motion, a body possesses translational kinetic energy ($K_t$) as well as rotational kinetic energy ($K_r$) simultaneously. The ratio $K_t : (K_t + K_r)$ for the sphere will be:
Consider a system of two particles having masses $m_1$ and $m_2$. If the particle of mass $m_1$ is pushed towards the centre of mass of particles through a distance $d$, by what distance would the particle of the mass $m_2$ move so as to keep the centre of mass of particles at the original position?
From a circular disc of radius $R$ and mass $9M$, a small disc of mass $M$ and radius $R/3$ is removed concentrically. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its centre is:
A transformer is used to light a 100 W and 110 V lamp from a 220 V main. If the main current is 0.5 A, the efficiency of the transformer is approximately:
An object flying in the air with velocity $(20\hat{i} + 25\hat{j} - 12\hat{k})$ suddenly breaks into two pieces whose masses are in the ratio of $1:5$. The smaller mass flies off with a velocity $(100\hat{i} + 35\hat{j} + 8\hat{k})$. The velocity of the larger piece will be:
A solid sphere, disc, and solid cylinder all of the same mass and made up of the same material are allowed to roll down (from rest) on an inclined plane, then:
Let En = -(me^4)/(8ε_0^2 n^2 h^2) be the energy of the nth level of H-atom. If all the H-atoms are in the ground state and radiation of frequency (E2 - E1)/h falls on it, then: (a) it will not be absorbed at all. (b) some of the atoms will move to the first excited state. (c) all atoms will be excited to the n=2 state. (d) no atoms will make a transition to the n=3 state. Choose the correct option:
The energy of ground electronic state of hydrogen atom is -13.6 eV. The energy of the first excited state will be:
Match List-I (Spectral Series) with List-II (corresponding wave number expressions). List-I (Series) A. Balmer series B. Lyman series C. Brackett series D. Pfund series List-II (Wave number in cm⁻¹) I. R(1/1² - 1/n²) II. R(1/4² - 1/n²) III. R(1/5² - 1/n²) IV. R(1/2² - 1/n²) Choose the correct answer from the options given below:
The photon radiated from hydrogen corresponding to the second line of Lyman series is absorbed by a hydrogen-like atom X in the second excited state. As a result the hydrogen-like atom X makes a transition to nth orbit. Then:
Three objects, $A$ (a solid sphere), $B$ (a thin circular disk) and $C$ (a circular ring), each have the same mass $M$ and radius $R$. They all spin with the same angular speed about their own symmetry axes. The amount of work ($W$) required to bring them to rest, would satisfy the relation:
The wavelength of the first spectral line in the Balmer series of hydrogen atom is 6561 Å. The wavelength of the second spectral line in the Balmer series of singly ionized helium atom is:
The total energy of an electron in the first excited state of hydrogen is about -3.4 eV. Its kinetic energy in this state is:
In the Bohr's model of a hydrogen atom, the centripetal force is furnished by the Coulomb attraction between the proton and the electron. If a₀ is the radius of the ground state orbit, m is the mass and e is the charge on the electron, ε₀ is the vacuum permittivity, the speed of the electron is:
Point masses $m_1$ and $m_2$ are placed at the opposite ends of a rigid rod of length $L$ and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point P on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity $\omega_0$ is minimum, is given by:
A thin circular ring of mass $M$ and radius $r$ is rotating about its axis with a constant angular velocity $\omega$. Four objects each of mass $m$, are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular velocity of the ring will be:
A disc and a solid sphere of the same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?
A black body at $227^\circ\text{C}$ radiates heat at the rate of $7 \text{ cal cm}^{-2}\text{s}^{-1}$. At a temperature of $727^\circ\text{C}$, the rate of heat radiated in the same units will be:
A constant torque of $100\text{ N m}$ turns a wheel of moment of inertia $300\text{ kg m}^2$ about an axis passing through its centre. Starting from rest, its angular velocity after $3\text{ s}$ is: