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The sum of moments of masses of all the ...

The sum of moments of masses of all the particles in a system about the center of mass is

A

minimum

B

maximum

C

zero

D

infinity

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The correct Answer is:
C
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Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass : (a) Show p=p_(i)'+m_(i)V where pi is the momentum of the ith particle (of mass m_(i) ) and p'_(i)=m_(i)v'_(i) . Note v'_(i) is the velocity of the ith particle relative to the centre of mass. Also, prove using the definition of the centre of mass sump'_(i)=O (b) Show K=K'+1//2MV^(2) where K is the total kinetic energy of the system of particles, K′ is the total kinetic energy of the system when the particle velocities are taken with respect to the centre of mass and MV^(2)//2 is the kinetic energy of the translation of the system as a whole (i.e. of the centre of mass motion of the system). The result has been used in Sec. 7.14. (c ) Show L=L'+RxxMV where L'=sumr'_(i)xxp'_(i) is the angular momentum of the system about the centre of mass with velocities taken relative to the centre of mass. Remember – r'_(i)=r_(i)-R , rest of the notation is the standard notation used in the chapter. Note ′ L and MR × V can be said to be angular momenta, respectively, about and of the centre of mass of the system of particles. (d) Show (dL')/(dt)=sumr'_(i)xx(dp')/(dt) Further, show that (dL')/(dt)=tau'_(ext) where tau'_(ext) is the sum of all external torques acting on the system about the centre of mass.

Suppose the particle of the previous problem has a mass m and a speed v before the collision and it sticks to the rod after the collision. The rod has a mass M. a. Find the velocity of the particle with respect to C of the system consituting the rod plus the particle. b. Find the velociyt of the particle with respect to C before the collision. c. Find the velocity of the rod with respect to C before the colision. e. find the moment of inertia of the system about the vertical axis through the centre of mass C after the collision. f. Find the velociyt of the centre of mass C and the angular velocity of the system about the centre of mass after the collision.

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FULL MARKS-MOTION OF SYSTEM OF PARTICLES AND RIGID BODIES-ADDITIONAL QUESTIONS SOLVED - I ( MULTIPLE CHOICE QUESTION)
  1. The distance between the centres of carbon and oxygen atoms in the gas...

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  2. The unit of position vector of center of mass is

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  3. The sum of moments of masses of all the particles in a system about th...

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  4. The motion of center of mass depends on

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  5. Two particles P and Q move towards with each other from rest with the ...

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  6. The reduced mass of the system of two particles of masses 2 m and 4 m ...

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  7. The motion of the center of mass of a system consists of many particle...

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  8. The positon of center of mass can be written in the vector form as

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  9. The positions of two masses, x1 and x2. The position of center of mass...

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  10. In a two particle system, one particle lies at origin another one lie...

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  11. State the principle of moments .

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  12. Infinitesimal quantity means

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  13. In the absence of external forces the center of mass will be in a stat...

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  14. The activity of the force to produce rotational motion in a body is ca...

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  15. The moment of the external applied force about a point or axis of rota...

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  16. Torque is given as

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  17. The magnitude of torque is

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  18. The direction of torque acts

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  19. The unit of torque is

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  20. The direction of torque is found using

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