JEE Advanced Systems of Particles and Rotational Motion — practice questions
116 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice JEE Advanced Systems of Particles and Rotational Motion in the app →The moment of inertia of a solid sphere of mass $M$ and radius $R$ about a diameter is:A particle of mass $m$ moves in a circle of radius $R$ with constant speed $v$. Its angular momentum about theA solid sphere of mass $M$ and radius $R$ rolls without slipping on a horizontal surface with translational spA thin uniform rod of mass $M$ and length $L$ rotates about an axis perpendicular to the rod and passing throuA solid sphere is released from rest at the top of an incline of angle $\theta$. If it rolls without slipping A solid disc and a thin ring, having the same mass and same radius, are released from rest at the top of the sThe **moment of inertia** of a thin uniform rod of mass $M$ and length $L$ about a perpendicular axis through The **angular momentum** of a particle of momentum $\vec p$ at position $\vec r$ (from origin) is:For a body **rolling without slipping** on a flat surface with centre-of-mass velocity $v$, the **velocity of A solid sphere ($I = \tfrac{2}{5}MR^2$) rolls without slipping down a plane inclined at $\theta$. Its **linearBy **parallel-axis theorem**, the moment of inertia of a thin ring of mass $M$, radius $R$, about a tangent inAn ice-skater spinning with arms extended ($I_1 = 4$ kg·m², $\omega_1 = 3$ rad/s) pulls her arms in to $I_2 = A uniform rod of length $L$ is suspended from one end. Its **time period** for small oscillations is:A coin sits at distance $r$ from the centre of a turntable rotating with angular speed $\omega$. The **maximumAn Atwood machine: masses $m_1 > m_2$ over a **massive** pulley (uniform disc, mass $M$, radius $R$, $I = MR^2Four objects roll without slipping down an identical incline from the same height: **solid sphere, solid cylinA **solid sphere** rolling without slipping enters a vertical loop of radius $R$. The **minimum height** $h$ fTwo coaxial discs ($I_1, I_2$ with angular velocities $\omega_1, \omega_2$) are suddenly coupled. **Energy disA **yo-yo** (solid uniform cylinder) of mass $M$, radius $R$ unwinds under gravity. Its downward acceleration A billiard ball of radius $R$, mass $m$ at rest is struck horizontally by an impulse $J$ at height $h$ above iA **uniform cube** of side $a$ sits on a rough incline. As $\theta$ is increased, the cube **topples** before A solid sphere rolls at speed $v$ on a horizontal surface and elastically collides with an identical stationarA **disc** of mass $M$, radius $R$ rolls without slipping. A particle of mass $m$ rests on its **top** (sticksA thin **rod of length $L$, mass $M$** is hinged at one end and held horizontally; released from rest. The **aA **uniform sphere** of radius $R$ and mass $M$ is placed inside a fixed hemispherical bowl of radius $5R$. FoA man of mass $m$ stands at the edge of a horizontal platform (mass $M$, radius $R$, moment $I = \tfrac{1}{2}MA **bullet** of mass $m$, velocity $v$ strikes the lower end of a uniform rod (mass $M$, length $L$, hinged atA **hollow sphere** ($I = \tfrac{2}{3}MR^2$) and a **solid sphere** of equal mass and radius roll without slipA wheel of radius $R$ rolls without slipping at speed $v$. The **velocity** of a point on the rim at angle $\pA horizontal disc of mass $M$, radius $R$ spins freely at $\omega$. A second identical disc is dropped verticaA solid sphere is placed on a horizontal surface with **initial linear velocity $v_0$ (forward) and zero angulA spool of inner radius $r$ and outer radius $R$ ($r < R$) rests on a rough horizontal floor. A thread is pullA child of mass $m$ runs tangentially at speed $v$ and jumps on the rim of a stationary playground merry-go-roA uniform circular disc of radius $R$ and mass $M$ has a circular hole of radius $R/2$ cut out, **centred** atAngular displacement theta in a circular motion is related to arc length s and radius r as:Angular velocity omega in terms of time period T:Linear speed v and angular speed omega relation for circular motion:Torque tau acting on a body produces:Angular momentum L of a body rotating with angular velocity omega:A wheel starting from rest reaches 20 rad/s in 4 s. Angular acceleration alpha:Moment of inertia of a uniform solid sphere of mass M and radius R about an axis through center:Moment of inertia of a thin uniform disc (mass M, radius R) about axis perpendicular to disc through center:Parallel axis theorem states I_parallel = I_cm + Md². Here d is:For a thin rod of mass M and length L, I about axis through center perpendicular to rod:Kinetic energy of a rotating body with moment of inertia I and angular velocity omega:For a body rolling without slipping with velocity v of center of mass:A solid cylinder and a hollow cylinder of same mass and radius roll down an incline. Which reaches bottom firsTwo point masses 3 kg each at the ends of a massless rod of length 4 m. I about axis through center perpendicuA figure skater pulls in her arms during a spin. Her moment of inertia decreases. By conservation of L (I × omFor a hoop, disc, and solid sphere of same mass and radius rolling down an incline. Order of acceleration (fasA solid sphere of mass M, radius R rolls without slipping down an incline of angle theta. Acceleration:Two point masses 3 kg each at the ends of a massless rod of length 4 m. I about axis through center perpendicuFor a thin rod (mass M, length L) about axis through ONE END perpendicular to rod, I equals:Torque on a body produces angular acceleration. For tau = 20 N m and I = 5 kg m², alpha equals:A 50 kg flywheel of radius 0.5 m rotates at 60 rev/min. Angular momentum (I = MR²/2):A solid sphere rolls down without slipping. Fraction of KE that is rotational:A man stands at center of a rotating platform with hands extended (I_initial). He brings hands closer to body A wheel rotating at 50 rad/s decelerates uniformly to rest in 10 s. Total angular displacement:Angular acceleration alpha = 4 rad/s² acts for 5 s on a wheel starting from rest. Number of revolutions:For a body rotating at constant angular velocity omega, the linear speed at distance r from the axis is v = omA solid cylinder (I = MR²/2) of mass 2 kg, radius 0.1 m, rolls without slipping at 6 m/s. Total kinetic energyA merry-go-round (I = 1000 kg m²) rotates at 0.5 rad/s. A 50 kg child runs and jumps onto it at radius 2 m. NeFor a solid cylinder rolling without slipping, the friction force at the contact point:Moment of inertia of an annular disc (inner radius r1, outer r2) about perpendicular axis through center:Per NCERT §6.2 eqn 6.1, the centre of mass of two particles m₁ at x₁ and m₂ at x₂ is which?Per NCERT §6.2, the centre of mass of THREE equal masses placed at the vertices of a triangle lies at which poPer NCERT §6.2, the centre of mass of a UNIFORM (homogeneous) symmetric body lies at which location?Per NCERT §6.3 eqn 6.11, the equation of motion of the centre of mass of a system of particles is which?Per NCERT §6.3, in a system on which no external force acts, the centre of mass does which?Per NCERT §6.4, the total LINEAR MOMENTUM of a system of particles equals which?Per NCERT §6.4 (Newton's 2nd law for CM), if F_ext on the system is zero, the total linear momentum of the sysPer NCERT Example 6.3 (L-shaped uniform lamina), if all three identical squares have equal mass, the CM coinciPer NCERT §6.2 (continuous body), the CM of a continuous distribution is given by which integral?Per NCERT §6.1.1, a rigid body's general motion can be decomposed into which two kinds?Per NCERT §6.2, when the origin of coordinates is chosen at the centre of mass, what does Σ m_i r_i equal?Per NCERT Ex 6.1, three particles of mass 100 g, 150 g, 200 g sit at the vertices of an equilateral triangle. Per NCERT §6.5, the magnitude of the VECTOR (cross) product A × B is which?Per NCERT §6.5, the vector product is which property algebraically?Per NCERT §6.5, the cross products î × ĵ, ĵ × k̂, k̂ × î equal which respectively?Per NCERT §6.6 eqn 6.19, the linear velocity of a particle of a rigid body rotating with angular velocity ω atPer NCERT §6.7.1, the TORQUE (moment of force) on a particle at position r due to force F is which vector prodPer NCERT §6.7.1, the SI unit of torque is which?Per NCERT §6.7.2 eqn 6.25a, the ANGULAR MOMENTUM of a particle of momentum p at position r is which?Per NCERT §6.7.2 eqn 6.26, the time derivative of angular momentum L of a particle equals which quantity?Per NCERT §6.7 (Conservation of L), if the total EXTERNAL torque on a system is zero, the total angular momentPer NCERT §6.7.2, the angular momentum L of a particle is zero when which of the following holds?Per NCERT §6.5, the cross product of two PARALLEL vectors is which?Per NCERT §6.7.1, the dimensions of torque (and angular momentum × time) are which?Per NCERT §6.9 eqn 6.34, the moment of inertia of a system of particles about an axis is which?Per NCERT §6.9 eqn 6.35, the ROTATIONAL kinetic energy of a body about a fixed axis is which?Per NCERT §6.9 (radius of gyration), if I = M k², then k represents which?Per NCERT Table 6.1, the moment of inertia of a thin RING of mass M and radius R about an axis ⊥ to its plane Per NCERT Table 6.1, the moment of inertia of a uniform DISC of mass M and radius R about its central axis (⊥ Per NCERT Table 6.1, the moment of inertia of a thin ROD of mass M and length L about an axis ⊥ to it through Per NCERT Table 6.1, the moment of inertia of a solid SPHERE of mass M and radius R about its diameter is whicPer NCERT Table 6.1, the moment of inertia of a SOLID cylinder of mass M and radius R about its own axis is whPer NCERT §6.9, the dimensions and SI unit of moment of inertia are which?Per NCERT §6.10, the rotational kinematic equation analogous to v = v₀ + at is which?Per NCERT §6.10, the rotational analogue of v² = v₀² + 2 a x is which?Per NCERT Example 6.11, a wheel spins up from 1200 rpm to 3120 rpm in 16 s. The angular acceleration is approxPer NCERT §6.11 eqn 6.41, the rotational analogue of Newton's second law (F = m a) for rotation about a fixed Per NCERT Table 6.2 (translational vs rotational), the rotational analogue of LINEAR MOMENTUM p = M v is whichPer NCERT §6.11, the WORK done by a torque τ over angular displacement θ is which?Per NCERT §6.11 eqn 6.40, the POWER delivered by a torque is which?Per NCERT §6.8 (equilibrium of a rigid body), a rigid body is in MECHANICAL equilibrium when which conditions Per NCERT §6.8.1 (principle of moments / lever), at equilibrium a lever satisfies which condition?Per NCERT §6.8.2, the CENTRE OF GRAVITY of an extended body in a UNIFORM gravitational field coincides with whPer NCERT §6.12 (and many examples), if an ice skater pulling arms inward DECREASES her moment of inertia, whaPer NCERT Example 6.12, a flywheel of M=20 kg, R=0.2 m has I = MR²/2 = which?Per NCERT Example 6.12, the angular acceleration of the same flywheel under a 25 N pull (τ = FR = 5 N m) is whPer NCERT Example 6.12, after 2 m of cord unwinds at 25 N pull, the work done by the pull is which?Per NCERT §6.11 (frictionless rigid body), the work done by an external torque equals which?A child pushes a door of width $0.8$ m perpendicular to the door at the handle with $20$ N force. The torque aA solid disc of mass $M$, radius $R$, rotating about its centre axis has moment of inertia:An ice skater spinning with arms outstretched at $\omega_1$ pulls arms in, halving her moment of inertia. Her A bicycle wheel of radius $R$ rolls without slipping at linear speed $v$. The angular speed $\omega$ is: