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The velocity of the CM of the sytem of p...

The velocity of the CM of the sytem of particle can be represented as :

A

`v _(CM) = ( sum m _(1) v _(1))/(m _(1))`

B

`v _(CM) = ( m _(1) v _(1))/(M)`

C

`v _(CM) = (sum m _(1) v _(1))/(M)`

D

None of the above

Text Solution

AI Generated Solution

To find the velocity of the center of mass (CM) of a system of particles, we can follow these steps: ### Step-by-Step Solution: 1. **Understanding the Center of Mass (CM)**: The center of mass of a system of particles is defined as a point that represents the average position of the mass distribution in the system. The position vector \( R_{cm} \) of the center of mass can be expressed as: \[ R_{cm} = \frac{\sum m_i r_i}{M} ...
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Knowledge Check

  • A particle executing simple harmonic motion with an amplitude 5 cm and a time period 0.2 s. the velocity and acceleration of the particle when the displacement is 5 cm is

    A
    `0.5pims^(-1),0ms^(-2)`
    B
    `0.5ms^(-1),-5pi^(2)ms^(-2)`
    C
    `0ms^(-1),-5pi^(2)ms^(-2)`
    D
    `0.5pims^(-1),-0.5pi^(2)ms^(-2)`

  • Mirror is moving towards the particle with speed 2 cm/sec. Speed of A ad B are 10sqrt(2) and 5 cm/sec respectively in the direction shown in figure. Magnitude of velocity of image of the particle B with respect to image of A.

    A
    `sqrt(325)cm//sec`
    B
    `15cm//sec`
    C
    `13cm//sec`
    D
    `sqrt(269)cm//sec`

  • Three forces start acting simultaneously on a particle moving with velocity vec(v) . These forces are represented in magnitude and direction by the three sides os a triangle ABC (as shown). The particle will now move with velocity.

    A
    `vec(v)` remaining unchanged
    B
    less than `vec(v)`
    C
    greater than `vec(v)`
    D
    `vec(v)` in the direction of the largest force BC

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