21 Official GATE PH Questions with Verified Solutions & Answer Keys
The moment of inertia of a uniform sphere of radius r about an axis passing through its centre 21 4 7t is given by 3 -rр) A rigid sphere of uniform mass density p and radius R has ...
A rigid body is rotating about its centre of mass, fixed at the origin, with an angular velocity ã and angular acceleration ã. If the torque acting on it is 7 and its angular momen...
The moment of inertia tensor of a rigid body is given by I= The magnitude of the -4 moment or meria about an axis i - ( 1 5, 0) is (A) 6 (B) 5 (C) 2 (D) 8/3...
A hoop of radius R is pivoted at a point on the circumference. The period of small oscillations in the plane of the hoop is (A) 2л 2R (B) 27 P8 (0) 278 (D) 27 28 PH 6/24 2008 MAIN ...
A heavy symmetrical top is rotating about its own axis of symmetry (the z-axis). If 1,,l, and 13 are the principal moments of inertia along x, y and z axes respectively, then (A) 1...
Two bodies of mass m and 2m are connected by a spring of spring constant k. The frequency of the normal mode is (A) V3k/2m (B) Vk/m (C) V2k/3m (D) Vk/2m...
Consider two small blocks, each of mass M, attached to two identical springs. One of the springs is attached to the wall, as shown in the figure. The spring constant of each spring...
The moment of inertia of a rigid diatomic molecule A is 6 times that of another rigid diatomic molecule B. If the rotational energies of the two molecules are equal, then the corre...
A two-dimensional square lattice has lattice constant a. k represents the wavevector in reciprocal space. The coordinates (kx, ky) of reciprocal space where band gap(s) can occur, ...
A material is placed in a magnetic field intensity H. As a result, bound current density J, is induced and magnetization of the material is M. The magnetic flux density is B. Choos...
Consider a point charge +Q of mass m suspended by a massless, inextensible string of length l in free space (permittivity o) as shown in the figure. It is placed at a height d (d >...
A system of two atoms can be in three quantum states having energies 0, € and Z€. The system is in equilibrium at temperature T = (kвB)-1 . Match the following Statistics with the ...
The wavefunction of a particle in a one-dimensional infinite well of size 2 a at a certain time is 𝜓(x) = 1 √8 √2sin ( \pi ) +√3cos ( \pi 2) + cos ( ^3\pi 2 ). Probability of find...
A piston of mass m is fitted to an airtight horizontal cylindrical jar. The cylinder and piston have identical unit area of cross-section. The gas inside the jar has volume V and i...
A particle of unit mass moves in a potential V(r) = -V_0e-^2 . If the angular momentum of the particle is L = 0.5ඥV_0 , then which of the following statements are true?...
In a diatomic molecule of mass M, electronic, rotational and vibrational energy scales are of magnitude E, E and EV, respectively. The spring constant for the vibrational energy is...
A symmetric top has principal moments of inertia I1 = I2 = 2\alpha 3 , I3 = 2\alpha about a set of principal axes 1, 2, 3 respectively, passing through its center of mass, where \a...
A system of f ive identical, non -interacting particles with mass m and spin 3 2 is confined to a one-dimensional potential well of length L. If the lowest energy of the system is ...
Two frames S (solid lines) and S' (dashed lines) with common origin are shown in the figure below. Frame S is inertial while S' is rotating about the common z-axis. There is a poin...
A symmetric rigid body has moment of inertia I1, I2, I3 about its principal axes 1, 2, and 3, respectively, with I1 = I3 = I⊥ and I2 ≠ I⊥. It is rotating in space with no torque on...
Rotational spectrum of a diatomic molecule consists of lines of equal spacing with an interval of 20.0 cm-1. Its moment of inertia is found to be I0 × 10-47kg. m2, the value of I0 ...