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A light and a heavy body have equal kinetic energy. Which one has a greater momentum?
A radioactive nucleus ${}_Z^A X$ undergoes spontaneous decay in the sequence ${}_Z^A X \to {}_{Z-1} B \to {}_{Z-3} C \to {}_{Z-2} D$, where $Z$ is the atomic number of element $X$. The possible decay particles in the sequence are
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:
Which amine reacts with Hinsberg's reagent to produce an alkali insoluble product?
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:
Dihedral angle of least stable conformer of ethane is :
The position of a particle is given by $\vec{r} = \hat{i} + 2\hat{j} - \hat{k}$ and momentum $\vec{P} = 3\hat{i} + 4\hat{j} - 2\hat{k}$. The angular momentum is perpendicular to:
A circular disk of moment of inertia $I_t$ is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed $\omega_i$. Another disk of moment of inertia $I_b$ is dropped coaxially onto the rotating disk. Initially the second disk has zero angular speed. Eventually both the disks rotate with a constant angular speed $\omega_f$. The energy lost by the initially rotating disc to friction is:
Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities $\omega_1$ and $\omega_2$. They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is:
Which of the following ecological pyramids is generally inverted?
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:
Two periodic waves of intensities $I_1$ and $I_2$ pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is: