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System of Particles and Rotational Motion · Question 71

AIPMT 2007MCQEasy📈 Topic in 12% papers+4−1
1

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 with respect to origin O is LA when it is at A and LB when it is at B, then [figure]

  1. LA = LB
  2. the relationship between LA and LB depends upon the slope of the line AB
  3. LA < LB
  4. LA > LB

Answer

(1) LA = LB

Solution

L = mv r , where r = perpendicular distance of the line of motion from O.

For every point on line AB, r = OC (same), and m, v are constant.

⇒ LA = mv(OC) = LB (same direction, along the z-axis)

Answer: (1)

AIPMT 2007

Keep practising — System of Particles and Rotational Motion

2

A uniform rod AB of length l and mass m is free to rotate about point A. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about A is ml23, the initial angular acceleration of the rod will be [figure]

  1. mgl2
  2. 32gl
  3. 3g2l
  4. 2g3l
AIPMT 2007
3

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

  1. 10
  2. 12
  3. 4
  4. 6
AIPMT 2007
4

A uniform rod AB of length l and mass m is free to rotate about point A. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about A is ml23, the initial angular acceleration of the rod will be

  1. mgl2
  2. 32gl
  3. 3g2l
  4. 2g3l
AIPMT 2006
5

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

  1. 12MR2
  2. MR2
  3. 25MR2
  4. 32MR2
AIPMT 2006
6

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

  1. MR2
  2. 12MR2
  3. 32MR2
  4. 72MR2
AIPMT 2005
7

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

  1. dissipates energy as heat
  2. decreases the rotational motion
  3. decreases the rotational and translational motion
  4. converts translational energy to rotational energy.
AIPMT 2005
8

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 velocity will be in the ratio

  1. 2 : 1
  2. 1 : 2
  3. 2 : 1
  4. 1 : 2
AIPMT 2005
9

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 [figure]

  1. 34ml2
  2. 2ml2
  3. 54ml2
  4. 32ml2
AIPMT 2004
10

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?

  1. m1m1 + m2d
  2. m1m2d
  3. d
  4. m2m1d
AIPMT 2004
11

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

  1. 2 15 N m
  2. 12 N m
  3. 15 N m
  4. 18 N m
AIPMT 2004

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