Q.1
A particle undergoes uniform circular motion. About which point on the plane of the circle, will the angular momentum of the particle remain conserved? [ IIT 2003]
  • a) centre of the circle
  • b) on the circumference of the circle
  • c) inside the circle
  • d) outside the circle
Q.2
A thin wire of length L and uniform linear mass density ρ is bent into a circular loop with centre at O as shown. The moment of inertia of the loop about the axis XX' is .. [ IIT 2000]
ch-6_que_no-65_img_no1.png
  • a)(ρL3)/ (8π2)
  • b) (ρL3)/ (16π2)
  • c)(5ρL3) / (16π2)
  • d)(3ρL3) / (8π2)
Q.3
An equilateral triangle ABC formed from a uniform wire has two small identical beads initially located at A. 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 the other along AC as shown. Neglecting frictional effects, the quantities that are conserved as the beads slide down are [ IIT 2000]
ch-6_que_no-66_img_no1.png
  • a) angular velocity and total energy ( kinetic and potential)
  • b) total angular momentum and total energy
  • c)angular velocity and moment of inertia about axis of rotation
  • d)total angular momentum and moment of inertia about axis of rotation
Q.4
One quarter sector is cut from a uniform circular disc of radius R. This sector has mass M. It is made to rotate about a line perpendicular to its plane and passing through the centre of the original to its plane and passing through the centre of the original disc. Its moment of inertia about the axis of rotation is .. [ IIT 2001]
ch-6_que_no-67_img_no1.png
  • a) ½ MR2
  • b) ¼ MR2
  • c)(1/8) MR2
  • d)√2 MR2
Q.5
Consider a body, shown in figure, consists of two identical balls, each of mass M connected by a rigid rod. If an impels J=MV is imparted to the body at one of its ends, What would be its angular velocity [ IIT 2003]
ch-6_que_no-68_img_no1.png
  • a) V/L
  • b) 2V/L
  • c) V/3L
  • d) V/4L
Q.6
A horizontal circular plate is rotating about a vertical axis passing through its centre with an angular velocity ωA man sitting at the centre having two blocks in his hands stretches out his hands so that the moment of inertia of the system doubles. If the kinetic energy of the system is K initially, its final kinetic energy will be [ IIT 2004]
  • a)2K
  • b) K/2
  • c)K
  • d)K/4
Q.7
A disc is rolling without slipping with angular velocity ω. P and Q are two points equidistant from the centre C. The order of magnitude of velocity is [ IIT 2004]
  • a) vQ > vC > vP
  • b)vP > vC > vQ
  • c)vP=vC , vQ=vC /2
  • d)vP < vC > vQ
Q.8
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 [ IIT 2005]
ch-6_que_no-71_img_no1.png
  • a)4MR2
  • b) (40/9)MR2
  • c)10 MR2
  • d)(37/9)MR2
Q.9
A particle is confined to rotate in a circular path decreasing linear speed, then which of the following is correct [ IIT 2005]
  • a) L angular momentum is conserved about the centre
  • b) only direction of angular momentum L is conserved
  • c) it spirals towards the centre
  • d) its acceleration is towards the centre
Q.10
A solid sphere of mass M and radius R having moment of inertia I about its diameter is recast into a solid disc of radius r and thickness t. The moment of inertia of the disc about an axis passing the edge and perpendicular to the plane remains I. Then R and r are related as [ IIT 2006]
  • a)r=√(2/15) × R
  • b) r=(2/√15) × R
  • c)r=(2/15) R
  • d)r=(√2 / 15)√R
Q.11
A small object of uniform density rolls up a curved surface with an initial velocity v. It reaches up maximum height of 3v2 / 4g with respect to the initial position. The object is [ IIT 2007]
ch-6_que_no-74_img_no1.png
  • a) ring
  • b) solid sphere
  • c)hollow sphere
  • d)disc
Q.12
A bob of mass M is suspended by the massless string of length L. The horizontal velocity v at position A is just sufficient to make it reach the point B. The angle θ t which the speed of the bob is half of that at A, satisfies.. [ IIT 2008]
ch-6_que_no-75_img_no1.png
  • a)θ=π/4
  • b) π/4 < θ < π/2
  • c)π/2 < (3/4)π
  • d)(3/4)π < θ < π
Q.13
Look at the drawing given in 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 segment is m. The mass of the ink used to draw the outer circle is 6m. The coordinates of the centres of the different parts are : Outer (0, 0), left circle (-a, a), right inner circle (a, a), vertical line (0,0) and horizontal line (0, -a). The y-coordinate of the centre of mass of the ink in this drawing is[ IIT 2009]
ch-6_que_no-76_img_no1.png
  • a) a/10
  • b) a/8
  • c) a/12
  • d) a/3
Q.14
Moment of inertia of a circular wire of mass M and radius R about its diameter is [ AIEEE 2002]
  • a)MR2 / 2
  • b) MR2
  • c)2MR2
  • d)MR2/4
Q.15
Two identical particles move towards each other with velocity 2v and v respectively. The velocity of centre of mass is [ AIEEE 2002]
  • a) v
  • b) v/3
  • c)v/2
  • d)zero
Q.16
A solid sphere, a hollow sphere and a ring are released from top of an inclined plane ( frictionless, so that they slide down the plane). Then maximum acceleration down the plane is for [ AIEEE 2002]
  • a)solid sphere
  • b) hollow sphere
  • c)ring
  • d)all same
Q.17
The minimum velocity(in m/s) with which a car driver must traverse a flat curve of radius 150m and coefficient of friction 0.6 to avoid skidding is [ AIEEE 2002]
  • a) 60
  • b) 30
  • c) 15
  • d) 25
Q.18
Four point masses, each of value m, are placed at the corners of square ABCD of side l. The moment of inertia of this system about an axis passing through A and parallel to BD. [ AIEEE 2006]
  • a)2ml2
  • b) √3 (ml2)
  • c)3ml2
  • d)ml2
Q.19
Angular moment of the particle rotating with a central force is constant due to [ AIEEE 2007]
  • a) constant torque
  • b) constant force
  • c)constant linear momentum
  • d)zero torque
Q.20
Consider a uniform square plate of side 'a' and mass 'm'. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of the axis perpendicular to its plane and passing through one of its corners is [ AIEEE 2008]
  • a)(5/6) m a2
  • b) (1/12)ma2
  • c)(7/12)ma2
  • d)(2/3)ma2
Q.21
Consider a two particle system with particles having masses m1 and mIf the first particle is pushed towards the centre of mass through a distance d, by what distance should the second particle is moved, so as to keep the centre of mass at the same position [ AIEEE 2006]
  • a) (m2 / m1 ) d
  • b) [m1 /(m1 + m2)] d
  • c) (m1 / m2) d
  • d) d
Q.22
The moment of inertia of a uniform semicircular disc of mass M and radius r about a line perpendicular to the plane of the disc through the centre is [ AIEEE 2005]
  • a)(2/5)Mr2
  • b) (1/4)Mr
  • c)(1/2)Mr2
  • d)Mr2
Q.23
A solid sphere is rotating in free space. if the radius of the sphere is increased keeping mass same which one of the following will not be affected? [ AIEEE 2004]
  • a) Angular velocity
  • b) Angular momentum
  • c)Moment of inertia
  • d)Rotational kinetic energy
Q.24
A particle performing uniform circular motion has angular frequency if doubled and its kinetic energy halved, then the new angular momentum is [ AIEEE 2003]
  • a) L/4
  • b) 2L
  • c)4L
  • d)L/2
Q.25
A body A of mass M while falling vertically downwards under gravity breaks into two parts, a body B of mass (1/3)M and a body C of masses (2/3)M. The centre of mass of body B and C taken together shifts compared to that of body A towards [ AIEEE 2005]
  • a) does not shift
  • b) depends on height of breaking
  • c) body B
  • d) body C
Q.26
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. [ AIEEE 2005]
ch-6_que_no-89_img_no1.png
  • a)(3/2)l
  • b) (2/3)l
  • c)l
  • d)(4/3)l
Q.27
A thin uniform rod of length l and mass m is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is ω. Its centre of mass rises to a maximum height of [ AIEEE 2009]
  • a)
    ch-6_qn-90choice_img_no1.png
  • b)
    ch-6_qn-90choice_img_no2.png
  • c)
    ch-6_qn-90choice_img_no3.png
  • d)
    ch-6_qn-90choice_img_no4.png
Q.28
A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincides. The centre of mass of the new disc is α/R from the centre of the bigger disc. The value of α is [ AIEEE 2007]
  • a) 1/4
  • b) 1/3
  • c)1/2
  • d)1/6
Q.29
For the given uniform square lamina ABCD, whose centre is O, [ AIEEE 2007]
ch-6_que_no-92_img_no1.png
  • a) IAC=√2 IEF
  • b) √2 IAC=IEF
  • c) IAD=3 IEF
  • d) I AC=IEF
Q.30
A circular disc X of radius R is made from iron plate of thickness t and another disc Y of radius 4R is made from an iron plate of thickness t/Then the relation between the moment of inertia Ix and Iy is [ AIEEE 2003]
  • a)IY=32IX
  • b) IY=16IX
  • c)IY=IX
  • d)IY=64IX
0 h : 0 m : 1 s