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

                 

  •   43l

  •   I

  •   23l

  •   32l

A wheel is rotating about an axis through its centre at 720 r.p.m. It is acted upon by a constant torque opposing its motion for 8 seconds to bring it to rest finally.The value of torque in Nm is: (given l = 24π kg m2)

  • 48

  • 72

  • 96

  • 120

Assertion : The speed of whirlwind in a tornado is alarmingly high.

Reason    : If no external torque acts on a body, its angular velocity remains conserved.

  • If both assertion and reason are true and reason is the correct explanation of assertion.

  • If both assertion and reason are true but reason is not the correct explanation of assertion.

  • If assertion is true but reason is false.

  • If both assertion and reason are false.

A circular disc A of radius r is made from an iron plate of thickness t and another circular disc B of radius 2r and thickness t4. The relation between moments of inertia IA and IB is

  •   IA > IB

  •   IA = IB

  •   IA < IB

  •   Depends on the actual values of t and r

A stationary bomb explodes into two parts of masses 3kg and 1kg. The total KE of the two parts after explosion is 2400 J. The KE of smaller part is 

  • 600 J

  • 1800 J

  • 1200 J

  • 2160 J

A particle of mass 2 kg located at the position (i^+ j^) m has a velocity of 2(+i^ - j^ +k^) m/s. Its angular momentum about z-axis in kg-m2/s is :

  • +4

  • +8

  • -4

  • -8

A cylinder of mass 'M' is suspended by two strings wrapped around it as shown. The acceleration 'a' and the tension T when the cylinder falls and the string unwinds itself are, respectively,
             

  •   a = g, T = Mg2

  •   a = g2, T = Mg2

  •   a = g3, T = Mg3

  •   a = 2g3, T = Mg6

An automobile engine develops 100 kW when rotating at a speed of 1800 rev/min. What torque does it deliver ?

  • 350 N-m

  • 440 N-m

  • 531 N-m

  • 628 N-m

In an orbital motion, the angular momentum vector is 

  • Along the radius vector

  • Parallel to the linear momentum

  • In the orbital plane

  • Perpendicular to the orbital plane

A particle of mass m moves with a constant velocityalong 3 different paths, DE, OA and BC. Which of the following statements is not correct about its angular momentum about point O?

                           

  • It is zero when it is at A and moving along OA.

  • The same at all points along the line DE.

  • Of the same magnitude but oppositely directed at B and  D.

  • Increases as it moves along the line BC.

A sphere is rolling down a plane of inclination θ to the horizontal.  The acceleration of its centre down the plane is 

  

  • g sin θ                   

  • less than g sin θ

  • greater than g sin θ

  • zero

A body at rest breaks into two pieces of equal masses.  The parts will move

 

  • in same direction

  • along different lines

  • in opposite directions with equal speeds

  • in opposite directions with unequal speeds

A bob of mass m attached to an inextensible string of length l is suspended from verticle support.  The bob rotates in a horizontal circle with an angular speed ω rad/s about the vertical.  About the point of suspension.

 

  • Angular momentum is conserved

  • Angular momentum changes in magnitude but not in the direction

  • Angular momentum changes in direction but not in magnitude

  • Angular momentum changes both in direction and magnitude 

In free space, a rifle of mass M shoots a bullet of mass m at a stationary block of mass M at a distance D away from it. When the bullet has moved through a distance d towards the block, the centre of mass of the bullet - block system is at a distance of

  •  (D-d)M+m from the bullet

  •  md+MDM+m from the block

  •  2md+MDM+m from the block

  •  (D-d)MM+m from the bullet

Blocks A and B are resting on a smooth horizontal surface given equal speeds of 2 m/s in the opposite sense as shown in the figure.

                           

At t = 0, the position of blocks are shown, then the coordinates of centre of mass at t = 3s will be 

  •   (1, 0)

  •   (3, 0)

  •   (5, 0)

  •   (2.25, 0)

A wheel is at rest. Its angular velocity increases uniformly and becomes 80 rad/s after 5 s. The total angular displacement is 

  • 800 rad

  • 400 rad

  • 200 rad

  • 100 rad

A force -Fk^ acts on O, the origin of the coordinate system. The torque at the point (1, -1) will be:

  •  -Fi^+j^

  •  Fi^+j^

  •  -Fi^-j^

  •  Fi^-j^

Moment of inertia of an object does not depend upon

  •   mass of object

  •   mass distribution

  •   angular velocity

  •   axis of rotation

A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its center and perpendicular to its plane with an angular velocity ω. Another disc of the same dimensions but of mass 14M is placed gently on the first disc co-axially.The angular velocity of the system will be:

  •   23ω

  •   45ω

  •   34ω

  •   13ω

When a ball of mass = 5kg hits a bat with a velocity = 3 m/s, in positive direction and it moves back with a velocity = 4 m/s, find the impulse in SI units

  • 15

  • 25

  • 35

When a torque acting upon a system is zero, then which of the following will be constant 

  •   force

  •   Linear momentum

  •   Angular momentum

  •   Linear impulse

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

  •   m1m1 + m2d

  •   m1m2d

  •   d

  •   m2m1d

The rotational KE of a body is E and its moment of inertia is I. The angular momentum is 

  •   EI

  •   2EI

  •   2 EI

  •   EI

If the linear density of a rod of length 3m varies as λ=2+x, then the position of the center of mass of the rod is at a distance of:

  •   73m

  •   107m

  •   127m

  •   97m

A flywheel is in the form of a uniform circular disc of radius 1 m and mass 2 kg. The work which must be done on it to increase its frequency of rotation from 5 rev s-1 to 10 rev s-1 is approximately

  •   1.5 x 102 J

  •   3.0 x 102 J

  •   1.5 x 103 J

  •   3.0 x 103 J

A particle of mass m has momentum p. it's kinetic energy will be 

  •   mp

  •   p2m

  •   p2m

  •   p22m

A constant torque acting on a uniform circular wheel changes its angular momentum from A0 to 4 A0 in 4s. The magnitude of this torque is 

  •  3A04

  •  4 A0

  •  A0

  •  12 A0

Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc D1 has 2 kg mass and 0.2 m radius and initial angular velocity of 50 rad s-1. Disc D2 has 4 kg mass, 0.1 m radius and initial angular velocity of 200 rad s-1. The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in rad.s-1) of the system is

  • 60

  • 100

  • 120

  • 40

A body rolls down an inclined plane without slipping. The fraction of total energy associated with its rotation will be

1. K2+ R22. K2R23. K2K2+ R24. R2K2+ R2

Where k is radius of gyration of the body about an axis passing through centre of mass and R is the radius of the body. 

  • 1
  • 2
  • 3
  • 4

A mass of 100 g strikes the wall with speed 5 m/s at an angle as shown in figure and it rebounds with the same speed. If the contact time is 2×10-3 s, what is the force applied on the mass by the wall

  •  2503 N to right

  • 250 N to right

  •  2503 N to left

  • 250 N to left

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