Home
Class 11
PHYSICS
Locate the center of mass....

Locate the center of mass.

Text Solution

Verified by Experts

(a) Take location of the leftmost particle as origin.
`{:(,x),(m,0),(2m ,L),(3m ,L + 2L=3L):}`
`x_(c.m.) = (m_(1) xx 0 + m_(2) xx d)/(m_(1) + m_(2)) = (m_(2) d)/(m_(1) + m_(2))`
( c) Take the bottommost particle as origin.
`{:(,y),(m , 0),(2m , L),(3m , L + 2L = 3L):}`
`y_(c.m.) = ( m xx 0 + 2m xx L + 3m xx 3L)/( m + 2m + 3m) = (11 mL)/(6 m) = (11 L)/(6)`


Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Locate the centre of mass of uniform triangular lamina and a uniform cone.

Locate the centre of mass of arrangement shown in figure. The three rods are identical in mass and length

Assertion: If there are no external forces, the center of mass of a double star moves like a free particle. Reason: If we go to the center of mass frame, then we find that the two stars are moving in a circle about the center of mass, which is at rest.

Three masses 3,4 and 5 kg are located at the corners of an equilateral triangle of side 1m. Locate to centre of mass of the system.

Find the Xcm of center of mass of a barbell consisting of 50kg and 80kg weights at the opposite ends of a 1.5-along bar of negligible mass. [Hint] Choosing the origin at one the masses here conveniently makes one of the terms in the sum Sigmam_(i)x_(i)zero . But, as always, the choice of origin is purely for convenience and doesn't influence that actual physical location of the center of mass.

The coordinates of the center of mass of the following quarter circular arc are

Find the velocity of the center of mass of the system shown in the figure .

The velocities of two particles of masses m_(1) and m_(2) relative to an observer in an inertial frame are v_(1) and v_(2) . Determine the velocity of the center of mass relative to the observer and the velocity of each particle relative to the center of mass.

Two balls are thrown simultaneously from top of tower in air as shown in the figure. (i) The acceleration of the center of mass of two balls while in air is equal to g . (ii) The path followed by the center of mass is parabola. (iii) The path followed by the center of mass will change if one ball after striking the ground comes to rest.

CP SINGH-CENTER OF MASS-Exercises
  1. Locate the center of mass.

    Text Solution

    |

  2. Two blocks of mass 1kg and 3 kg have position v ectors hat(i) + 2 hat...

    Text Solution

    |

  3. All the particles of a body situated at distance d from the origin. Th...

    Text Solution

    |

  4. Particle of masses m, 2m,3m,…,nm grams are placed on the same line at ...

    Text Solution

    |

  5. Three identical metal balls each of radius r are placed touching each ...

    Text Solution

    |

  6. Look at the drawing given in the figure which has been drawn with ink ...

    Text Solution

    |

  7. A circular disc of radius R is removed from a bigger circular disc of ...

    Text Solution

    |

  8. A hemisphere and a solid cone have a common base. The center of mass o...

    Text Solution

    |

  9. If the linear density (mass per unit length) of a rod of length 3 m is...

    Text Solution

    |

  10. The mass per unit length of a non - uniform rod of length L is given m...

    Text Solution

    |

  11. A thin rod of length 'L' is lying along the x-axis with its ends at x...

    Text Solution

    |

  12. Which of the following is true for center of mass ? (i) The center o...

    Text Solution

    |

  13. A cubical block of ice of maas m and edge L is placed in a large tray ...

    Text Solution

    |

  14. Two paricle A and B initially at rest, move towards each other under m...

    Text Solution

    |

  15. A ladder is leaned against a smooth wall and it is allowed to slip on ...

    Text Solution

    |

  16. A pulley fixed to the ceiling carries a string with blocks of mass m a...

    Text Solution

    |

  17. Two balls are thrown simultaneously from top of tower in air as shown ...

    Text Solution

    |

  18. Which of the following statements are true ? (i) A uniform wooden pl...

    Text Solution

    |

  19. Which of the following statements is true ? (i) A car of mass M is t...

    Text Solution

    |

  20. A boy of mass 40 kg stands on a rail road car of mass 60 kg, moving wi...

    Text Solution

    |

  21. A boy (mass of 40 kg) is standing at one end of a boat (mass of 60 kg)...

    Text Solution

    |