AIPMT-PRELIMS Physics System of Particles and Rotational Motion Class 11 Questions

ABC is an equilateral triangle with O as its centre. F̅₁, F̅₂ and F̅₃ represent three forces acting along the sides AB, BC and AC respectively. If the total torque about O is zero then the magnitude of F̅₃ is

When a mass is rotating in a plane about a fixed point, its angular momentum is directed along:

A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is 45°, the speed of the car is

Two persons of masses 55 kg and 65 kg respectively, are at the opposite ends of a boat. The length of the boat is 3.0 m and weighs 100 kg. The 55 kg man walks up to the 65 kg man and sits with him. If the boat is in still water the centre of mass of the system shifts by

The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is I₀. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is

The instantaneous angular position of a point on a rotating wheel is given by the equation θ(t) = 2t² – 6t². The torque on the wheel becomes zero at

A particle moves in a circle of radius 5 cm with constant speed and time period 0.2 π s. The acceleration of the particle is

A gramophone record is revolving with an angular velocity ω. A coin is placed at a distance r from the centre of the record. The static coefficient of friction is μ. The coin will revolve with the record if

A circular disk of moment of inertia I₁ is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed ω₀. 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 ω_r. The energy lost by the initially rotating disc to friction is

Two particles which are initially at rest, move towards each other under the action of their internal attraction. If their speeds are v and 2v at any instant, then the speed of centre of mass of the system will be

A thin circular ring of mass M and radius R is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity ω. If two objects each of mass m be attached gently to the opposite ends of a diameter of the ring, the ring will then rotate with an angular velocity:

If \( \vec{F} \) is the force acting on a particle having position vector \( \vec{r} \) and \( \vec{\tau} \) be the torque of this force about the origin, then:

Four identical thin rods each of mass M and length ℓ, form a square frame. Moment of inertia of this frame about an axis through the centre of the square and perpendicular to its plane is :

Two bodies of mass 1 kg and 3 kg have position vectors î + 2ĵ + k̂ and −3î − 2ĵ + k̂, respectively. The centre of mass of this system has a position vector:

A thin rod of length L and mass M is bent at its midpoint into two halves so that the angle between them is 90°. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is -

A roller coaster is designed such that riders experience 'weightlessness' as they go round the top of a hill whose radius of curvature is 20m. The speed of the car at the top of the hill is between -

The ratio of the radii of gyration of a circular disc to that of a circular ring, each of same mass and radius around their respective axes is -

A wheel has angular acceleration of 3.0 rad/sec² and an initial angular speed of 2.0 rad/sec. In a time of 2 sec it has rotated through an angle (in radian) of

Weight of the rod will produce torque, τ = mg × ℓ/2. Also, τ = Iα. Where, I is the moment of inertia = mℓ²/3 and α is the angular acceleration. Therefore, mℓ²/3 α = mg × ℓ/2 ⇒ α = 3g/2ℓ.

Angular momentum = Linear momentum × distance of line of action of linear momentum about the origin.

The moment of inertia of a uniform circular disc of radius R and mass M about an axis touching the disc at its diameter and normal to the disc is:

A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity ω. The force exerted by the liquid at the other end is:

A uniform rod of length l and mass m is free to rotate in a vertical plane about A. The rod initially in horizontal position is released. The initial angular acceleration of the rod is: (Moment of inertia of rod about A is (ml²/3))

A drum of radius R and mass M, rolls down without slipping along an inclined plane of angle θ. The frictional force:

A stone tied to the end of a string of 1 m long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolutions in 44 s, what is the magnitude and direction of acceleration of the stone ?

Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio:

The moment of inertia of a uniform circular disc of radius R and mass M about an axis passing from the edge of the disc and normal to the disc is:

The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is:-

A round disc of moment of inertia I₂ about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia I₁ rotating with an angular velocity ω about the same axis. The final angular velocity of the combination of discs is :-

Three particles, each of mass m gram, are situated at the vertices of an equilateral triangle ABC of side ℓ cm. (as shown in the figure). The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC, in gram cm² units will be :-

A wheel having moment of inertia 2 kg–m² about its vertical axis, rotates at the rate of 60 rpm about the axis. The torque which can stop the wheel's rotation in one minute would be :-

Consider a system of two particles having masses m₁ and m₂. If the particle of mass m₁ is pushed towards the mass centre of particles through a distance 'd', by what distance would the particle of mass m₂ move so as to keep the mass centre of particles at the original position :-

A particle moves along a circle of radius (20/π) m with constant tangential acceleration. If the velocity of the particle is 80 m/s at the end of the second revolution after motion has begun, the tangential acceleration is :

A thin circular ring M and radius ‘r’ is rotating about its axis with a constant angular velocity ω. 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 solid cylinder of mass M and radius R rolls without slipping down an inclined plane of length L and height h. What is the speed of its centre of mass when the cylinder reaches its bottom -

A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is K. If radius of the ball be R, then the fraction of total energy associated with its rotational energy will be :

A circular disc is to be made by using iron and aluminium so that it acquired maximum moment of inertia about geometrical axis. It is possible with :-

A disc is rotating with angular speed ω. If a child sits on it, what is conserved :-

A point P consider at contact point of a wheel on ground which rolls on ground without sliping then value of displacement of point P when wheel completes half of rotation (If radius of wheel is 1m) :-

A rod of length is 3m and its mass acting per unit length is directly proportional to distance x from one of its end then its centre of gravity from that end will be at :-

Two particles having mass 'M' and 'm' are moving in a circular path having radius R & r respectively. If their time period are same then the ratio of angular velocity will be:

A disc is rolling the velocity of its centre of mass is V_cm then which one will be correct :-

A mass is performing vertical circular motion (see figure). If the average velocity of the particle is increased, then at which point the string will break:

For a hollow cylinder & a solid cylinder rolling without slipping on an inclined plane, then which of these reaches earlier on the ground :

For the adjoining diagram, a triangular lamina is shown the correct relation between I₁, I₂ & I₃ is (I – moment of inertia)