JEE Questions for Physics Systems Of Particles And Rotational Motion Quiz 3

Two solid cylinders P and Q of same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder P has most of its mass concentrated near its surface, while Q has most of its mass concentrated near the axis. Which statements (s) is (are) correct ?

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Both cylinders P and Q reach the ground at the same time
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Cylinder P has larger linear acceleration than cylinder Q
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Both cylinders reach the ground with same translational kinetic energy
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Cylinder Q reaches the ground with larger angular speed

A thin ring of mass 2 kg and radius 0.5 m is rolling without slipping on a horizontal plane with velocity 1 m/s. A small ball of mass 0.1 kg, moving with velocity 20 m/s in the opposite direction, hits the ring at a height of 0.75 m and goes vertically up with velocity 10 m/s. Immediately after the collision
Physics-Systems of Particles and Rotational Motion-88748.png

Physics-Systems of Particles and Rotational Motion-88748.png

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the ring has pure rotation about its axis
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the ring comes to a complete stop
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friction between the ring the ground is to the left
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there is no friction between the ring and the ground

Look at the drawing given in the figure, which has been drawn with ink of uniform line thickness. The mass of ink used to draw each of the two inner circles and each of the two line segments is m. The mass of the ink used to draw the outer circle is 6 m.
The coordinates of the centres of the different parts are outer circle (0,left inner circle (– a, a), right inner circle (a, a), vertical line (0,and horizontal line (0, –a). The y – coordinate of the centre of mass of the ink in this drawing is
Physics-Systems of Particles and Rotational Motion-88750.png

Physics-Systems of Particles and Rotational Motion-88750.png

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A pulley fixed to the ceiling carries a string with blocks of masses m and 3m attached to its ends. The masses of string and pulley are negligible. When the system is released, the acceleration of centre of mass will be

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zero
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The figure shows a system consisting of (i) a ring of outer radius 3R rolling clockwise without slipping on a horizontal surface with angular speed w and (ii) an inner disc of radius 2R rotating anti–clockwise with angular speed w/ 2 .
The ring and disc are separated by frictionless ball bearings. The system is in the x–z plane. The point P on the inner disc is at a distance R from the origin, where OP makes an angle of 30° with the horizontal. Then with respect to the horizontal surface,
Physics-Systems of Particles and Rotational Motion-88760.png

Physics-Systems of Particles and Rotational Motion-88760.png

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A T shaped object with dimensions shown in the figure, is lying on a smooth floor. A force F is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. Find the location of P with respect to C.
Physics-Systems of Particles and Rotational Motion-88766.png

Physics-Systems of Particles and Rotational Motion-88766.png

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Physics-Systems of Particles and Rotational Motion-88772.png

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Physics-Systems of Particles and Rotational Motion-88778.png

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Physics-Systems of Particles and Rotational Motion-88784.png

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5 unit
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Given data is not correct

Three identical spheres of mass M each are placed at the corners of an equilateral triangle of side 2 m. Taking one of the corner as the origin, the position vector of the centre of mass is

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Physics-Systems of Particles and Rotational Motion-88793.png

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depends on height of breaking
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does not shift
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body C
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body B

Two balls each of mass m are placed on the vertices A and Bof an equilateral triangle ABC of side 1 m. A ball of mass 2m is placed at vertex C. The centre of mass of this system from vertex A (located at origin) is
Physics-Systems of Particles and Rotational Motion-88795.png

Physics-Systems of Particles and Rotational Motion-88795.png

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Four thin rods of same mass M and same length l, form a square as shown in the figure. Moment of inertia of this system about an axis through centre O and perpendicular to its plane is
Physics-Systems of Particles and Rotational Motion-88801.png

Physics-Systems of Particles and Rotational Motion-88801.png

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A solid sphere of mass M, radius R and having moment of inertia about an axis passing through the centre of mass as I, is recast into a disc of thickness t, whose moment of inertia about an axis passing through its edge and perpendicular to its plane remains I. Then, radius of the disc will be

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Physics-Systems of Particles and Rotational Motion-88812.png

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A thin wire of length l having density ρ is bent into a circular loop with C as its centre, as shown in the figure. The moment of inertia of the loop about the line AB is
Physics-Systems of Particles and Rotational Motion-88818.png

Physics-Systems of Particles and Rotational Motion-88818.png

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A lamina is made by removing a small disc of diameter 2R from a bigger disc of uniform mass density and radius 2R, as shown in the figure. The moment of inertia of this lamina about axes passing through 0 and P is I_o and I_p , respectively. Both these axes are perpendicular to the plane of the lamina.
Physics-Systems of Particles and Rotational Motion-88824.png

Physics-Systems of Particles and Rotational Motion-88824.png

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3
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Let F be the force acting on a particle having position vector r and τ be the torque of this force about the origin. Then,

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Each of the body in List I shows the moment of inertia about its diameter in List II. Select the correct answer (matching List I with List II) as per code given below the lists.
Physics-Systems of Particles and Rotational Motion-88826.png

Physics-Systems of Particles and Rotational Motion-88826.png

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A = 2, B = 3, C = 1
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A = 3, B = 2, C = 1
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A = 3, B = 1, C = 2
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A =1, B = 2, C = 3

One solid sphere A and another hollow sphere B are of same mass and same outer radius. Their moments of inertia about their diameters are respectively I_A and I_B such that
Note: d_A and d_B are their densities.

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IA = IB
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IA > IB
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IA < IB
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The moment of inertia of a thin uniform rod of length L and mass M about an axis passing through a point at a distance of 1/3 from one of its ends and perpendicular to the rod is

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Moment of inertia of a rod of mass M and length L about an axis passing through a point midway between centre and end is

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From a disc of radius R, a concentric circular portion of radius r is cut out so as to leave an annular disc of mass M. The moment of inertia of this annular disc about the axis perpendicular to its plane and passing through its centre of gravity is

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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

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The moment of inertia of a solid sphere of mass M and radius R about the tangent on its surface is

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Physics-Systems of Particles and Rotational Motion-88855.png

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For the given uniform square lamina ABCD, whose centre is O
Physics-Systems of Particles and Rotational Motion-88861.png

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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

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Two solid spheres (A and B) are made of metals of different densities ρ_A and ρ_B respectively. If their masses are equal, the ratio of their moments of inertia (I_B / I_B ) about their respective diameters is
Physics-Systems of Particles and Rotational Motion-88872.png

Physics-Systems of Particles and Rotational Motion-88872.png

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A solid sphere of radius R has moment of inertia I about its geometrical axis. If it is melted into a disc of radius r and thickness t. If its moment of inertia about the tangential axis (which is perpendicular to plane of the disc), is also equal to I, then the value of r is equal to
Physics-Systems of Particles and Rotational Motion-88878.png

Physics-Systems of Particles and Rotational Motion-88878.png

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Four point masses, each of value m, are placed at the corners of a square ABCD of side l. The moment of inertia of this system about an axis passing through A and parallel to BD is

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The moment of inertia of a circular disc about an axis which is tangential to the circumference of the disc and parallel to its diameter is

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Physics-Systems of Particles and Rotational Motion-88894.png

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5 R
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A T joint is formed by two identical rods A and B each of mass m and length L in the X – Y plane as shown. Its moment of inertia about axis coinciding with A is
Physics-Systems of Particles and Rotational Motion-88899.png

Physics-Systems of Particles and Rotational Motion-88899.png

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None of these

From a circular disc of radius R and mass 9M, a small disc of radius R/3 is removed from the disc. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through O is
Physics-Systems of Particles and Rotational Motion-88904.png

Physics-Systems of Particles and Rotational Motion-88904.png

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Moment of inertia of a disc about an axis which is tangent and parallel to its plane is I. Then the moment of inertia of disc about a tangent, but perpendicular to its plane will be

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For spheres each of mass M and radius R are placed with their centres on the four corners A , B, C and D of a square of side b. The spheres A and B are hollow and C and D are solids. The moment of inertia of the system about side AD of square is

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Physics-Systems of Particles and Rotational Motion-88920.png

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Angular momentum L is given by L =p.r. The variation of log Land log p is shown by
Physics-Systems of Particles and Rotational Motion-88926.png

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I
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II
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III
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IV

A small mass m is attached to a massless string whose other end is fixed at P as shown in the figure. The mass is undergoing circular motion in the x-y plane with centre at O and constant angular speed ω. If the angular momentum of the system, calculated about O and P are denoted by L_o and L_p respectively, then
Physics-Systems of Particles and Rotational Motion-88928.png

Physics-Systems of Particles and Rotational Motion-88928.png

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Lo and Lp do not vary with time
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Lo varies with time while Lp remains constant
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Lo remains constant while Lp varies with time
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Lo anad Lp both vary with time.

A thin uniform rod, pivoted at O, is rotating in the horizontal plane with constant angular speed ω, as shown in the figure. At time t = 0, a small insect starts from O and moves with constant speed v w.r.t. the rod towards the other end. It reaches the end of the rod at t =T and stops. The angular speed of the system remains ω throughout. The magnitude of the torque |τ| on the system about O, as a function of time is best represented by which plot ?
Physics-Systems of Particles and Rotational Motion-88930.png

Physics-Systems of Particles and Rotational Motion-88930.png

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A force F= 2.0 N acts on a particle P in the x – z plane. The force F is parallel to x-axis. The particle P (as shown in the figure) is at a distance 3 m and the line joining P with the origin makes angle 30° with the x-axis. The magnitude of torque on P w.r.t. origin O (in N–m) is
Physics-Systems of Particles and Rotational Motion-88936.png

Physics-Systems of Particles and Rotational Motion-88936.png

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A binary star consists of two stars A (mass 2.2M_s ) and B (mass 11M_s), where M_s is the mass of the sun. They are separated by distance d and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star to the angular momentum of star B about the centre of mass is

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7
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9
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10

A uniform disc of mass M and radius R is mounted on a fixed horizontal axis. A block of mass m hangs from a massless string that is wrapped around the rim of the disc. The magnitude of the acceleration of the falling block (m) is

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Physics-Systems of Particles and Rotational Motion-88949.png

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A uniform disc of mass 2 kg and radius 15 cm is revolving around the central axis by 4 rad s ^-1. The linear momentum of disc will be

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1.2 kg–ms-1
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1.0 kg–ms-1
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0.6 kg–ms-1
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None of these

A thin circular ring of mass M and radius R rotates about an axis through its centre and perpendicular to its plane, with a constant angular velocity ω. Four small spheres each of mass m (negligible radius) are kept gently to the opposite ends of two mutually perpendicular diameters of the ring. The new angular velocity of the ring will be

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A particle of mass m moves in the XY plane with a velocity v along the straight line AB. If the angular momentum of the particle w.r.t. origin O is LA, when it is at A and LB when it is at B, then
Physics-Systems of Particles and Rotational Motion-88962.png