Q.1
A mass m rotating freely in horizontal circle of radius 1m on frictionless smooth table supports a stationary mass 2m, attached to the other end of the string passing through smooth hole O in the table, hanging vertically. Find the angular velocity of rotation
ch-6_que_no-179_img_no1.png
  • a)√(2g)
  • b)√(g)
  • c)√(3g)
  • d)√(4g)
Q.2
Three particles of the same mass lie in the (X, Y) plane, The (X, Y) coordinates of their positions are (1, 1), (2, 2) and (3, 3) respectively. The (X,Y) coordinates of the centre of mass are
  • a) (1, 2)
  • b) (2, 2)
  • c) (1.5, 2)
  • d) (2, 1.5)
Q.3
A Pulley of radius 2 m is rotated about its axis by a force F = (20 t - 5t2 ) N where t is in sec applied tangentially. If the moment of inertia of the Pulley about its axis of rotation is 10 Kgm2 , the number of rotations made by the pulley before its direction of motion is reversed is
  • a) more than 3 but less then 6
  • b) more than 6 but less then 9
  • c) more than 9
  • d) Less then 3
Q.4
A cubical block of side a is moving with velocity V on a horizontal smooth plane as shown in figure. It hits a ridge at point O. The angular speed of the block after it hits O is ...
ch-6_que_no-182_img_no1.png
  • a) 3V/4a
  • b) 3V/2a
  • c) √(3V)/ √(2a)
  • d) zero
Q.5
Two uniform rod of equal length but different masses are rigidly joined to form L shaped body which is then pivoted as shown. If in equilibrium the body is in the shown configuration ratio M/m will be ..
ch-6_que_no-183_img_no1.png
  • a) 2
  • b) 3
  • c) √2
  • d) √3
Q.6
A light rod carries three equal masses A, B and C as shown in the figure the velocity of B in vertical position of rod if it is released from horizontal position as shown in the figure is ...
ch-6_que_no-184_img_no1.png
  • a)
    ch-6_qn-184choice_img_no1.png
  • b)
    ch-6_qn-184choice_img_no2.png
  • c)
    ch-6_qn-184choice_img_no3.png
  • d)
    ch-6_qn-184choice_img_no4.png
Q.7
Two identical hollow spheres of mass M and radius R are joined together and the combination is rotated about an axis tangential to one sphere and perpendicular to the line connecting their centres. The moment of inertia of the combination is ________.
ch-6_que_no-185_img_no1.png
  • a)10 MR2
  • b) (4/3) MR2
  • c)(32/3) MR2
  • d)(34/3) MR2
Q.8
A force F = αi + 3j + 6k is acting at a point r=2i-6j-12k. The value of α for which angular momentum about origin is conserved is
  • a) 1
  • b) -1
  • c) 2
  • d) zero
Q.9
Two point masses of 0.3 kg and 0.7 kg are fixed at the ends of a rod of length 1.4 m and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum, is located at a distance of …..
  • a) 0.4 m from mass of 0.3 kg
  • b) 0.98 m from mass of 0.3 kg
  • c)0.7 m from mass of 0.7 kg
  • d)0.98 m from mass of 0.7 kg
Q.10
A smooth sphere A is moving on a friction-less horizontal plane with angular speed ωand centre of mass velocity v. It collides elastically and head on with an identical sphere B at rest. Neglect friction everywhere. After the collision, their angular speeds are ωA and ωB respectively, Then
  • a) ωA < ωB
  • b) ωA=ωB
  • c) ωA=ω
  • d) ω=ωB
Q.11
Consider a body as shown in figure, consisting of two identical balls, each of mass M connected by a light rigid rod. If an impulse J=MV is imparted to the body at one of its ends, what would be its angular velocity. What is V ?
ch-6_que_no-188_img_no1.png
  • a) V / L
  • b) 2V / L
  • c) V / 3L
  • d) V / 4L
Q.12
A solid cylinder of mass M and radius R rolls down an inclined plane of height h. The angular velocity of the cylinder when it reaches the bottom of the plane will be.
  • a)
    ch-6_qn-189choice_img_no1.png
  • b)
    ch-6_qn-189choice_img_no2.png
  • c)
    ch-6_qn-189choice_img_no3.png
  • d)
    ch-6_qn-189choice_img_no4.png
Q.13
Two disc of same thickness but of different radii are made of two different materials such thattheir masses are same. The densities of the materials are in the ratio 1:The moment of inertiaof these disc about the respective axes passing through their centres and perpendicular to theirplanes will be in the ratio.
  • a) 1 : 3
  • b) 3 : 1
  • c)1 : 9
  • d)9 : 1
Q.14
Identify the correct statement for the rotational motion of a rigid body
  • a) Individual particles of the body do not undergo accelerated motion
  • b) The centre of mass of the body remains unchanged.
  • c)The centre of mass of the body moves uniformly in a circular path
  • d) Individual particle and centre of mass of the body undergo an accelerated motion
Q.15
A cylinder of mass 5 kg and radius 30 cm, and free to rotate about its axis, receives an angularimpulse of 3 kg m2s-1 initially followed by a similar impulse after every 4 sec. what is the angularspeed of the cylinder 30 sec after initial impulse ? The cylinder is at rest initially.
  • a) 106.7 rad s-1
  • b) 206.7 rad s-1
  • c) 7.6 rad s-1
  • d) 07.6 rad s-1
Q.16
A uniform rod of length L is suspended from one end such that it is free to rotate about anax is passing through that end and perpendicular to the length, what maximum angular speed must be imparted to the lower end so that the rod completes one full revolution?
  • a)√(g/l)
  • b) √(2g/l)
  • c)√(6g/l)
  • d)2√(g/l)
Q.17
Consider a two-particle system with the particles having masses M1 , and M2 . If the firstparticle is pushed towards the centre of mass through a distance d, by what distance shouldthe second particle be moved so as to keep the centre of mass at the same position?
  • a)
    ch-6_qn-194choice_img_no1.png
  • b)
    ch-6_qn-194choice_img_no2.png
  • c)
    ch-6_qn-194choice_img_no3.png
  • d)
    ch-6_qn-194choice_img_no4.png
Q.18
The moment of inertia of a thin rod of mass M and length L about an axis passing through thepoint at a distance L/4 from one of its ends and perpendicular to the rod is _____
  • a)(7ML2)/48
  • b)(ML2)/ 12
  • c)(ML2)/ 9
  • d)(ML2)/ 3
Q.19
The height of a solid cylinder is four times that of its radius. It is kept vertically at time t=0 on a belt which is moving in the horizontal direction with a velocity v=2.45t2 where v in m/sand t is in second. If the cylinder does not slip, it will topple over a time t=____
  • a) 1 second
  • b) 2 sec.
  • c) 3 sec.
  • d) 4 sec.
Q.20
A uniform rod of length 2L is placed with one end in contact with horizontal and is then inclined at an angle α to the horizontal and allowed to fall without slipping at contact point. When it becomes horizontal, its angular velocity will be…..
  • a)
    ch-6_qn-197choice_img_no1.png
  • b)
    ch-6_qn-197choice_img_no2.png
  • c)
    ch-6_qn-197choice_img_no3.png
  • d)
    ch-6_qn-197choice_img_no4.png
Q.21
In a bicycle the radius of rear wheel is twice the radius of front wheel. If Rf and Rr are the radius, Vf and Vr are speed of top most points of wheel respectively then...
  • a) Vr=2Vf
  • b) Vf=2Vr
  • c)Vf=Vr
  • d)Vf > Vr
Q.22
The M.I. of a body about the given axis is 1.2 kgm2 initially the body is at rest. In order to produce a rotational kinetic energy of 1500 J. an angular acceleration of 25rad sec-2 must be applied about that axis for duration of ….
  • a) 4 sec
  • b) 2 sec
  • c)8 sec
  • d)10 sec
Q.23
Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle of θ with AB. The moment of inertia of the plate about the axis CD is then equal to ...
  • a) I
  • b) I sin2θ
  • c) I cos2θ
  • d) I cos2(θ/2)
Q.24
An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 ms-1 and the second part of mass 2 kg moves with 8 ms-1 speed. If the third part flies off with 4 ms–1 speed, then its mass is … [ NEET 2013]
  • a) 3 kg
  • b) 5 kg
  • c) 7 kg
  • d) 17 kg
Q.25
A small object of uniform density rolls up a curvedsurface with an initial velocity v. It reaches up to amaximum height of with respect to the initialposition. The object is …. [ NEET 2013]
ch-6_que_no-202_img_no1.png
  • a) Ring
  • b) Solid sphere
  • c) Hollow sphere
  • d) Disc
Q.26
) A solid cylinder of mass 50 kg and radius0.5mis free to rotate about the horizontal axis. A massless string it wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions s-2 is … [ AIPMT 2014]
  • a) 78.5 N
  • b) 157 N
  • c) 25 N
  • d) 50 N
Q.27
The ratio of the accelerations for a solid sphere(mass 'm' and radius 'R') rolling down an incline of angle 'θ'with out slipping and slipping down the incline without rolling is
  • a) 2 : 5
  • b) 7 : 5
  • c) 5 : 7
  • d) 2 : 3
Q.28
A mass m moves in a circle on a smooth horizontal plane with velocity v0 at a radius RThe mass is attached to a string which passes through a smooth hole in the plane as shown. The tension in the string is increased gradually and finally m moves in a circle of radius R0/The final value of the kinetic energy
ch-6_que_no-205_img_no1.png
  • a)
    ch-6_qn-205choice_img_no1.png
  • b)
    ch-6_qn-205choice_img_no2.png
  • c)
    ch-6_qn-205choice_img_no3.png
  • d)
    ch-6_qn-205choice_img_no4.png
Q.29
Three identical spherical shells, each of mass m and radius r are placed as shown in figure. Consider an axis XX’ which is touching to two shells and passing through diameter of third shell. Moment of inertia of the system consisting of these three spherical shells about XX’ axis is :
ch-6_que_no-206_img_no1.png
  • a) 4mr2
    ch-6_qn-206choice_img_no2.png
  • b)
    ch-6_qn-206choice_img_no4.png
  • c) 3mr2
  • d)
Q.30
Two spherical bodies of mass M and 5 M and radii R and 2 R 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 before collision is :
  • a) 1.5 R
  • b) 2.5 R
  • c) 4.5 R
  • d) 7.5 R
0 h : 0 m : 1 s