List of top Physics Questions on Mechanics and General Properties of Matter

An unstable particle created at a point P moves with a constant speed of 0.998c until it decays at a point Q. If the lifetime of the particle in its rest frame is 632ns, the distance between points P and Q is ______m. (Rounded off to the nearest integer)
(c=3×108 m/s)

The moment of inertia of a solid hemisphere (mass 𝑀 and radius 𝑅) about the axis passing through the hemisphere and parallel to its flat surface is \(\frac{2}{5}\) 𝑀𝑅² . The distance of the axis from the center of mass of the hemisphere (in units of 𝑅) is______. (Rounded off to two decimal places)

The inertial frame 𝑆' is moving away from the inertial frame S with a speed 𝑣 = 0.6𝑐 along the negative x-direction (see figure). The origins 𝑂’ and 𝑂 of the frames coincide at 𝑡=𝑡’=0. As observed in the frame 𝑆′, two events occur simultaneously at two points on the 𝑥′-axis with a separation of ∆𝑥′=5m. If, ∆𝑡 and ∆𝑥 are the magnitudes of the time interval and the space interval, respectively, between the events in S, then which of the following statements is(are) correct?

(c = 3×10⁸ m/s)

A particle of mass m, having an energy E and angular momentum L, is in a parabolic trajectory around a planet of mass M. If the distance of the closest approach to the planet is r_m, which of the following statement(s) is(are) true?
(G is the Gravitational constant)

A spring-mass system (spring constant 80N/m and damping coefficient 40N-s/m), initially at rest, is lying along the y-axis in the horizontal plane. One end of the spring is fixed and the mass (5kg) is attached at its other end. The mass is pulled along the y-axis by 0.5m from its equilibrium position and then released. Choose the correct statement(s).
(Ignore mass of the spring)

An incompressible fluid is flowing through a vertical pipe (height h and crosssectional area 𝐴_𝑜). A thin mesh, having n circular holes of area 𝐴_ℎ is fixed at the bottom end of the pipe. The speed of the fluid entering the top-end of the pipe is 𝑣_𝑜. The volume flow rate from an individual hole of the mesh is given by:
(g is the acceleration due to gravity)

A tank, placed on the ground, is filled with water up to a height ℎ. A small hole is made at a height ℎ1 such that ℎ1 < ℎ. The water jet emerging from the hole strikes

the ground at a horizontal distance D, as shown schematically in the figure. Which of the following statements is correct? (g is the acceleration due to gravity)

The total number of Na and Cl ions per unit cell of the NaCl crystal is:

If the ground state energy of a particle in an infinite potential well of width L₁ is equal to the energy of the second excited state in another infinite potential well of width L₂, then the ratio \(\frac{L_1}{L_2}\) is equal to

Which of the following statements about the viscosity of a dilute ideal gas is correct ?

A container is occupied by a fixed number of non-interacting particles. If they are obeying Fermi-Dirac, Bose-Einstein, and Maxwell-Boltzmann statistics, the pressure in the container is P_FD, P_BE and P_MB, respectively. Then

A rod of mass 𝑀, length 𝐿 and non-uniform mass per unit length \(λ(x)=\frac{3Mx^2}{L^3},\) is held horizontally by a pivot, as shown in the figure, and is free to move in the plane of the figure. For this rod, which of the following statements are true?

A particle (𝑝₁) of mass 𝑚 moving with speed 𝑣 collides with a stationary identical particle (𝑝₂). The particles bounce off each other elastically with 𝑝₁ getting deflected by an angle 𝜃 = 30° from its original direction. Then, which of the following statement(s) is/are true after the collision?

For a particle moving in a general central force field, which of the following statement(s) is/are true?

The lattice constant (in Å) of copper, which has FCC structure, is _________ (rounded off to two decimal places).
Given: density of copper is 8.91 g cm^-3 and its atomic mass is 63.55 g mol^-1 ; Avogadro’s number = 6.023 × 10²³ mol⁻¹

Consider a spring mass system with mass 0.5 kg and spring constant 𝑘 = 2 Nm^-1 in a viscous medium with drag coefficient 𝑏 = 3 kg s ^-1 . The additional mass required so that the motion becomes critically damped is _______ kg (rounded off to three decimal places)

Consider the 𝛼-decay ⁹⁰𝑇ℎ ²³²→⁸⁸𝑅𝑎 ²²⁸ . In an experiment with one gram of ⁹⁰𝑇ℎ ²³², the average count rate (integrated over the entire volume) measured by the 𝛼-detector is 3000 counts s ^-1 . If the half life of ⁹⁰𝑇ℎ ²³² is given as 4.4 × 10¹⁷ s, then the efficiency of the 𝛼-detector is ______(rounded off to two decimal places).
Given: Avogadro’s number = 6.023 × 1023 mol⁻¹

Three frames 𝐹₀, 𝐹₁ and 𝐹₂ are in relative motion. The frame 𝐹₀ is at rest, 𝐹₁ is moving with velocity 𝑣1𝑖̂with respect to 𝐹₀ and 𝐹₂ is moving with velocity 𝑣₂𝑖̂ with respect to 𝐹₁. A particle is moving with velocity 𝑣3𝑖̂ with respect to 𝐹₂. If 𝑣₁ = 𝑣₂ = 𝑣₃= \(\frac{𝑐}{2}\), where 𝑐 is the speed of light, the speed of the particle with respect to 𝐹₀ is 𝑓𝑐. The value of 𝑓 is ____________ (rounded off to two decimal places)

A fission device explodes into two pieces of rest masses 𝑚 and 0.5𝑚 with no loss of energy into any other form. These masses move apart respectively with speeds \(\frac{c}{ √13} \) and \(\frac{c}{2}\) , with respect to the stationary frame. If the rest mass of the device is 𝑓𝑚 then 𝑓 is________ (rounded off to two decimal places).

Consider a particle trapped in a three-dimensional potential well such that U(x, y, z) = 0 for 0 ≤ x ≤ a, 0 ≤ y ≤ a, 0 ≤ z≤a and U(x, y, z) = ∞ everywhere else. The degeneracy of the 5^th excited state is

A particle of mass m and angular momentum L moves in space where its potential energy is U(r) = kr² (k > 0) and r is the radial coordinate.
If the particle moves in a circular orbit, then the radius of the orbit is

Consider a two-dimensional force field
\(\overrightarrow{F}(x,y) = (5x^2 + ay^2 + bxy)\hat{x} + (4x^2 + 4xy + y^2) \hat{y}\).
If the force field is conservative, then the values of a and b are

Consider a particle of mass m moving in a plane with a constant radial speed \(\dot{r}\) and a constant angular speed \(\dot{\theta}\). The acceleration of the particle in (r,\(\theta\)) coordinates is

Three masses $m_1$ = 1, $m_2$ = 2 and $m_3$ = 3 are located on the x-axis such that their center of mass is at x = 1. Another mass $m_1$ = 4 is placed at x, and the new center of mass is at x = 3. The value of $x_0$ is.