Home
Class 11
PHYSICS
A uniform rod of length L and mass M is ...

A uniform rod of length `L` and mass `M` is pivoted freely at one end and placed in vertical position.
a. What is angular acceleration of the rod when it is at an angle `theta` with the vertical?
b. What is the tangential linear acceleration of the free end when the rod is horizontal?

A

`gsintheta`

B

`g/Lsintheta`

C

`(3g)/(2L) sintheta`

D

`6gLsintheta`

Text Solution

Verified by Experts

The correct Answer is:
C
The moment of inertia of the uniform rod about an axis through one end and perpendicular to length is
`I=(ML^(2))/3`
Torque `(t=Ia)` acting on the gravity of the rod is given by
`tau=Mg [L/2sintheta]`
or `(ML^(2))/3alpha=Mg L/2 sintheta`
`alpha=(3g)/(2L)sintheta`
Promotional Banner

Topper's Solved these Questions

  • RIGID BODY DYNAMICS 1

    CENGAGE PHYSICS ENGLISH|Exercise Multiple Correct|9 Videos

  • RIGID BODY DYNAMICS 1

    CENGAGE PHYSICS ENGLISH|Exercise Linked Comprehension|28 Videos

  • RIGID BODY DYNAMICS 1

    CENGAGE PHYSICS ENGLISH|Exercise Subjective|13 Videos

  • PROPERTIES OF SOLIDS AND FLUIDS

    CENGAGE PHYSICS ENGLISH|Exercise INTEGER_TYPE|2 Videos

  • RIGID BODY DYNAMICS 2

    CENGAGE PHYSICS ENGLISH|Exercise Interger|2 Videos

Similar Questions

Explore conceptually related problems

A rod of length L is hinged from one end. It is brought to a horizontal position and released. The angular velocity of the rod, when it is in vertical position, is

A uniform thin rod of length l and mass m is hinged at a distance l//4 from one of the end and released from horizontal position as shown in Fig. The angular velocity of the rod as it passes the vertical position is

A uniform rod of mass 20 Kg and length 1.6 m is piovted at its end and swings freely in the vertical plane. Angular acceleration of the rod just after the rod is relased from rest in the horizontal position is

A L shaped rod of mass M is free to rotate in a vertical plane about axis A A as shown in figure. Maximum angular acceleration of rod is

A uniform rod of length l and mass m is free to rotate in a vertical plane about A as shown in Fig. The rod initially in horizontal position is released. The initial angular acceleration of the rod is

A slender uniform rod of mass M and length l is pivoted at one end so that it can rotate in a vertical plane, Fig. There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle theta with the vertical is

A rod of length L is hinged from one end. It is brought to the horizontal position and released. The angular velocity of the rod when it is in the vertical position is sqrt(Kg//L) . Then find the value of K.

A uniform rod of mass m and length L is hinged about one end and can freely rotate in a vertical plane. The angular velocity of the rod, when it falls from position P to Q. through an angle alpha starting from rest, is

A uniform rod of mass m length l is attached to smooth hinge at end A and to a string at end B as shown in figure. It is at rest. The angular acceleration of the rod just after the string is cut is :

A rod of mass m and length l is rotating about a fixed point in the ceiling with an angular velocity omega as shown in the figure. The rod maintains a constant angle theta with the vertical. What is the rate of change of angular momentum of the rod ?

CENGAGE PHYSICS ENGLISH-RIGID BODY DYNAMICS 1-Single Correct
  1. The moment of inertia of a solid sphere about an axis passing through ...

    Text Solution

    |

  2. A triangular plate of uniform thickness and density is made to rotate ...

    Text Solution

    |

  3. A uniform rod of length L and mass M is pivoted freely at one end and ...

    Text Solution

    |

  4. In Fig, the bar is uniform and weighing 500 N. How large must W be if ...

    Text Solution

    |

  5. In an experiment with a beam balance, an unknown mass m is balanced by...

    Text Solution

    |

  6. A sphere is moving towards the positive x-axis with a velocity v(c) an...

    Text Solution

    |

  7. A cylinder of height H and diameter H//4 is kept on a frictional turnt...

    Text Solution

    |

  8. A thin rod of length 4l, mass 4 m is bent at the point as shown in the...

    Text Solution

    |

  9. Three point masses m(1), m(2) and m(3) are located at the vertices of ...

    Text Solution

    |

  10. The pulleys in figure are identical, each having a radius R and moment...

    Text Solution

    |

  11. A uniform cube of side a and mass m rests on a rough horizontal table....

    Text Solution

    |

  12. A ladder of length l and mass m is placed against a smooth vertical wa...

    Text Solution

    |

  13. A cube of side a is placed on an inclined plane of inclination theta. ...

    Text Solution

    |

  14. A uniform rod of length l is placed symmetrically on two walls as show...

    Text Solution

    |

  15. A square plate of mass M and edge L is shown in the figure. The moment...

    Text Solution

    |

  16. The figure shows a uniform rod lying along the X-axis. The locus of al...

    Text Solution

    |

  17. Find the minimum height of the obstacle so, that the sphere can stay i...

    Text Solution

    |

  18. A sphere is placed rotating with its centre initially at rest in a cor...

    Text Solution

    |

  19. In the figure shown, the instantaneous speed of end A of the rod is v ...

    Text Solution

    |

  20. A uniform rod of mass m and length l is fixed from Point A, which is a...

    Text Solution

    |