JEE Questions for Physics Systems Of Particles And Rotational Motion Quiz 15 - MCQExams.com

A cricket bat is cut at the location of its centre of mass as shown. Then
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  • The two pieces will have the same mass
  • The bottom piece will have larger mass
  • The handle piece will have larger mass
  • Mass of handle piece is double the mass of bottom piece
Two particles of masses m1 and m2 initially at rest start moving towards each other under their mutual force of attraction. The speed of the centre of mass at any time t, when they are at a distance r apart, is
  • Zero
  • 2)
    Physics-Systems of Particles and Rotational Motion-90206.png

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

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  • d

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A man weighing 80 kg is standing in a trolley weighing 320 kg. The trolley is resting on frictionless horizontal rails. If the man starts walking on the trolley with a speed of 1 m/s, then after 4 sec his displacement relative to the ground will be
  • 5 m
  • 4.8 m
  • 3.2 m
  • 3.0 m
A cart of mass M is tied by one end of a massless rope of length 10 m. The other end of the rope is in the hands of a man of mass M. The entire system in on a smooth horizontal surface. The man is at x = 0 and the cart at x = 10 m. If the man pulls the cart by the rope, the man and the cart will meet at the point
  • x = 0
  • x = 5m
  • x = 10m
  • They will never meet
A system consisting of two masses connected by a massless rod lies along the x-axis. A 0.4 kg mass is at a distance x = 2 m while a 0.6 kg mass is at a distance x = 7m. The x-coordinate of the centre of mass is
  • 5 m
  • 3.5 m
  • 4.5 m
  • 4 m
  • 3 m
Three masses of 2 kg, 4 kg and 4 kg are placed at the three points ( 1, 0, 0), (1, 1,and (0, 1,respectively. The position vector of its centre of mass is

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A man of 50 kg mass it standing in gravity free space at a height of 10 m above the floor. He throws a stone of 0.5 kg mass downwards with a speed of 2 m/s. When the stone reached the floor, the distance of the man above the floor will be
  • 20 m
  • 9.9 m
  • 10.1 m
  • 10 m

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  • 10/3
  • 5/2
  • 1/2
  • 2/5
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 weight 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
  • 3.0 m
  • 2.3 m
  • zero
  • 0.75 m
A wheel is rolling along the ground with a speed of 2 ms–1. The magnitude of the velocity of the points at the extremities of the horizontal diameter of the wheel is equal to

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A point P on the rim of wheel is initially at rest and in contact with the ground. Find the displacement of the point P if the radius of the wheel is 5 m and the wheel rolls forward through half a revolution
  • 5 m
  • 10 m
  • 2.5 m

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A wheel has angular acceleration of 3.0 rad/sec2 and an initial angular speed of 2.00 rad/sec. In a time of 2 sec it has rotated through an angle (In radian) of
  • 6
  • 10
  • 12
  • 4
When a ceiling fan is switched on, it makes 10 revolutions in the first 3 seconds. Assuming a uniform angular acceleration, how many rotations it will make in the next 3 seconds?
  • 10
  • 20
  • 30
  • 40
A rectangular block has a square base measuring a × a, and its height is h. It moves on a horizontal surface in a direction perpendicular to one of its edges. The coeffiient of friction is μ. It will topple if

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The moment of inertia of a disc of mass M and radius R about an axis, which is tangential to circumference of disc and parallel to its diameter is

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Find the centre of mass of a metal circular sheet of diameter 6 cm, which has a 2 cm square cut out of it. The two sides of the square lie along diameters of the circle. OM is bisector of ∠AOD, Fig.
Physics-Systems of Particles and Rotational Motion-90377.png
  • At 5 cm from O towards B
  • At the centre of the circle
  • At 0.233cm from O towards M
  • At 3 cm from O towards A
A solid sphere is rotating about a diameter due to increase in room temperature, its volume increases by 5%, If no external torque acts. The angular speed of the sphere will.
  • increase by nearly 1/3 %
  • decrease by nearly 1/3 %
  • increase by nearly 1⁄2 %
  • decrease nearly by 1⁄2 %
The general motion of a rigid body can be considered to be a combination of (i) a motion of its centre of mass about an axis, and (ii) its motion about an instantaneous axis passing through the centre of mass.
These axes need not be stationary. Consider, for example, a thin uniform disc welded (rigidly fixed) horizontally at its rim to a massless stick, as shown in the figure.
When the disc-stick system is rotated about the origin on a horizontal frictionless plane with angular speed co, the motion at any instant can be taken as a combination of (i) a rotation of the centre of mass of the disc about the z-axis, and (ii) a rotation of the disc through an instantaneous vertical axis passing through its centre of mass (as is seen from the changed orientation of points P and Q).
Both these motions have the same angular speed ω this case.
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  • It is vertical for both the cases A and B.
  • It is vertical for case A and is at 45° to the x–z plane and lies in the plane of the disc for case B.
  • It is horizontal for case A and is at 45° to the x–z plane and is normal to the plane of the disc for case B.
  • It is vertical for case A and is at 45° to the x–z plane and is normal to the plane of the disc for case B.
The general motion of a rigid body can be considered to be a combination of (i) a motion of its centre of mass about an axis, and (ii) its motion about an instantaneous axis passing through the centre of mass.
These axes need not be stationary. Consider, for example, a thin uniform disc welded (rigidly fixed) horizontally at its rim to a massless stick, as shown in the figure.
When the disc-stick system is rotated about the origin on a horizontal frictionless plane with angular speed co, the motion at any instant can be taken as a combination of (i) a rotation of the centre of mass of the disc about the z-axis, and (ii) a rotation of the disc through an instantaneous vertical axis passing through its centre of mass (as is seen from the changed orientation of points P and Q).
Both these motions have the same angular speed ω this case.
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A small cone filled with water is revolved in a vertical circle of radius 4 m and the water does not fall down. What must be the maximum period of revolution?
  • 4 sec
  • 2 sec
  • 1 sec
  • 6 sec
Three point masses m1, m2 and m3 are placed at the corners of a thin massless rectangular sheet (1.2m × 1.0m), as shown in Fig. The centre of mass of the system is located at the point with coordinates
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  • (0.8, 0.m
  • (0.6, 0.m
  • (0.4, 0.m
  • (0.5, 0.m
A circular plate of uniform thickness has a diameter of 56 cm. A circular portion of diameter 42 cm is removed from one edge as shown in Fig. The centre of mass of the remaining portion from the centre of plate will be at
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  • 5 cm
  • 7 cm
  • 9 cm
  • 11 cm
A ring of mass m and radius r rotates about an axis passing through its centre and perpendicular to its plane with angular velocity ω. Its K.E. is
  • 0.5 mrω2
  • 0.5 mr2ω2
  • mrω2
  • mr2ω2
AB and CD are two identical rods each of length l and mass m joined to form a cross. The moment of inertia of these two rods about a bisector (XY) of angle between the rods is
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Three identical bricks of length l are placed on the top of each other as shown in Fig, so that the part of each overhangs the one below. Find in terms of l, the maximum value of the total overhung x.
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In a metallic triangular sheet ABC, AB = BC = l. If M is mass of sheet what is its moment of inertia about AC, Fig ?
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A rigid spherical body is spinning around an axis without any external torque. Due to change in temperature, the volume increases by 1%. Its angular speed will
  • increase approximately by 1%
  • decrease approximately by 1%
  • decrease approximately by 0.67%
  • decrease approximately by 0.33%
A thin circular ring of mass M and radius R is rotating about its axis with a constant angular speed ω. Two blocks each of mass m are attached gently to opposite ends of a diameter of the ring. The angular speed of the ring will be

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One end of a uniform rod of length l and mass m is hinged at A. It is released from rest from horizontal position AB as shown in Fig. The force exerted by the rod on the hinge when it becomes vertical is
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  • 3/2 mg
  • 3 mg
  • 5 mg
  • 5/2 mg
A uniform rod of mass m and length l is suspended by means of two light inextensible strings as shown in Fig. Tension in one string immediately after the other string is cut is
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  • mg/2
  • mg
  • 2mg
  • mg/4
A force F is applied at the top of a ring of mass M and radius R placed on a rough horizontal surface as shown in Fig. Friction is sufficient to prevent slipping. The frictional force acting on the ring is
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  • F/2 towards right
  • F/3 towards left
  • 2F/3 towards right
  • zero
An equilateral triangle ABC formed from a uniform wire has two small identical beads initially located at A, Fig. The triangle is set rotating about the vertical axis AO. Then the beads are released from rest simultaneously and allowed to slide down, one along AB and other along AC. Neglecting frictional effects, the quantities that are conserved as the beads slide down are
Physics-Systems of Particles and Rotational Motion-90291.png
  • angular velocity and total energy (K.E.+P.E.),
  • total angular momentum and total energy,
  • angular velocity and moment of inertia about the axis of rotation,
  • total angular momentum and moment of inertia about the axis of rotation.
A thin wire of length L and uniform linear mass density ρ is bent into a circular loop with centre at O, as shown in Fig. The moment of inertia of the loop about the axis XX’ is
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A circular platform is free to rotate in a horizontal plane about a vertical axis passing through its centre. A tortoise is sitting at the edge of the platform. Now the platform is given an angular velocity ω0. When the tortoise moves along a chord of the platform with a constant velocity (w.r.t. the platform), the angular velocity of the platform will vary with the time t as

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Two spherical bodies of masses M and 5 M and radii R and 2 R respectively are released in free space with initial separation between their centres equal to 12 R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is
  • 2.5 R
  • 4.5 R
  • 7.5 R
  • 1.5 R
Three particles, each of mass m gram, are situated at the vertices of an equilateral triangle ABC of side l cm as shown in Fig. The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC, in gram-cm2 will be
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From a circular disc of radius R and mass 9 M, a small disc of radius R/3 is removed. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through O is
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A ladder is leaned against a smooth wall and it is allowed to slip on a frictionless floor. Which figure represents trace of its centre of mass ?

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Three identical spheres, each of mass 1 kg are kept as shown in the Fig, touching eachother, with their centres on a straight line. If their centres are marked P, Q, R respectively, the distance of centre of mass of the system from P is
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    Physics-Systems of Particles and Rotational Motion-90334.png

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Four holes of radius R are cut from a thin square plate of side 4 R and mass M. The moment of inertia of the remaining portion about Z-axis is
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A disc of radius R rolls on a horizontal ground with linear acceleration a and angular acceleration α as shown in Fig., The magnitude of acceleration of point P at an instant, when its linear velocity is υ and angular velocity is ω will be
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    Physics-Systems of Particles and Rotational Motion-90346.png

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Two thin discs each of mass M and radius r metre are attached as shown to form a rigid body. The rotational inertia of this body about an axis perpendicular to the plane of disc B and passing through its centre is
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  • 2 Mr2
  • 3 Mr2
  • 4 Mr2
  • 5 Mr2
The moment of inertia of a uniform rod of length 2 l and mass m about an axis xx passing through its centre and inclined at an angle α is
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    Physics-Systems of Particles and Rotational Motion-90354.png

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A cube is placed on an inclined plane of inclination θ as shown in Fig. Coefficient of friction between the cube and the plane is μ. As angle θ is gradually increased, the cube slides before toppling if
Physics-Systems of Particles and Rotational Motion-90358.png
  • μ > 1
  • μ > 1/2
  • μ < 1/2
  • μ < 1
A horizontal turn table in the form of a disc of radius r carries a gun at G and rotates with angular velocity ω0 about a vertical axis passing through the centre O. The increase in angular velocity of the system if the gun fires a bullet of mass m with a tangential velocity υ w.r.t the gun is (where I0 is moment of inertia of gun + table, about O)
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A sphere is rotating between two rough inclined walls as shown in Fig. Coefficient of friction between each wall and the sphere is 1/3. If f1 and f2 be the frictional forces at P and Q, then f1/f2 is
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