Tag: center of mass

Questions Related to center of mass

A football rolls through the ground. The path followed by center of mass of football is:

physics turning effects of forces stability and centre of mass center of mass centre of mass

  1. linear

  2. circular

  3. rotational

  4. all the above

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Correct Option: A
Explanation:

When a football rolls through the ground, the path followed by center of mass of ball is linear as the center of mass remains always at a fixed height from the ground when the football rolls and moves in a straight line if the ball does not changes its direction of rolling which is assumed in this case.

The correct option is A.

which of these represent the centre of mass for a semicircular ring ?

physics turning effects of forces stability and centre of mass center of mass centre of mass

  1. $0$

  2. $\dfrac { 4R }{ 3\pi } $

  3. $\dfrac{R}{2}$

  4. $\dfrac { 2R }{ \pi } $

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Correct Option: B

A flexible chain of length 2m and mass 1 kg initially held in vertical position such that its lower end just touches a horizontal surfaces, is released from rest at time t=0, Assuming that any part of chain which strike the plane immediately comes to rest and that the portion of chain lying on horizontal surface does not form  any heap, the height of its center of mass above surface at any instant $t=1/\sqrt { 5 } $(before it completely comes to rest) is

physics turning effects of forces stability and centre of mass center of mass centre of mass

  1. 1 m

  2. 0.5 m

  3. 1.5 m

  4. 0.25 m

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Correct Option: A

A metallic ball has spherical cavity at its centre. If the ball is heated, what happens to the cavity?

physics turning effects of forces stability and centre of mass center of mass centre of mass

  1. its volume increases

  2. its volume decreases

  3. its volume remains unchanged

  4. its volume may decreased or increase depending upon the nature of metal

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Correct Option: A

A body having it's center of mass  at the origin. Then,

(The question having a multiple answers).

physics turning effects of forces stability and centre of mass center of mass centre of mass

  1. x co-ordinates of the particles may be all positive.

  2. total KE must be conserved.

  3. total KE must very.

  4. total momentum shall vary.

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Correct Option: C,D
Explanation:

If all the particles have positive x  co-ordinates then their COM can't be at the origin. Total KE may not be conserved because of internal forces. Its not given that there is no external force acting on the system, so its momentum may also change.

Where will be the centre of mass on combining two masses $m$ and $M(M>m)$ ?

physics turning effects of forces stability and centre of mass center of mass centre of mass

  1. $Towards \ m$

  2. $Towards \ M$

  3. $ exactly \ between \ m \ and \ M $

  4. $None \ of \ the \ above$

Show answer
Correct Option: B
Explanation:

As we can see that the center of mass will be at $r _c=\dfrac{mr+MR}{m+M}$,


where $r$ and $R$ are the position of the masses $m$ and $M$ respectively.

From the formula we notice that it will be between $m$ and $M$ and $nearer $ to the higher mass $M$.

A body has its center of mass at the origin. The x-axis coordinates of the particles :

physics turning effects of forces stability and centre of mass center of mass centre of mass

  1. may be all positive

  2. may be all negative

  3. should be all at zero

  4. may be positive for some case and negative in other cases.

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Correct Option: D
Explanation:

All co-ordinates positive will make the co-ordinate of com positive.
All co-ordinates negative will make the co-ordinates of com negative.
If all the co-ordinates are zero(0), co-ordinate of com is zero(0).
If  co-ordinate of com can be zero,  co-ordinates of some are positive and co-ordinates of some are negative.

If the linear density of a rod of length L varies as $\lambda =A+B _x$, compute its centre of mass.

physics turning effects of forces stability and centre of mass center of mass centre of mass

  1. $[\cfrac {L(3A+2BL)}{3(2A+BL},0,0]$

  2. $[0,\cfrac {(3A+2B)L}{(2A+3L},\cfrac L 2]$

  3. $[0,0\cfrac {L(3A+2BL)}{3(2A+BL}]$

  4. $[\cfrac L 2,00]$

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Correct Option: A

If a square of side $\dfrac{R}{2}$ is removed from a uniform circular disc of radius R as shown in the figure, the shift in centre of mass is 

physics turning effects of forces stability and centre of mass center of mass centre of mass

  1. $\dfrac{R}{4 \pi - 1}$

  2. $\dfrac{R}{2(4 \pi - 1)}$

  3. $\dfrac{R}{3(4 \pi - 1)}$

  4. $\dfrac{R}{4(4 \pi - 1)}$

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Correct Option: B

Which of the following is not correct about centre of mass ?

physics turning effects of forces stability and centre of mass center of mass centre of mass

  1. It depends on the choice of frame of reference

  2. In centre of mass frame, momentum of a system is always zero

  3. Internal forces may affect the motion of centre of mass

  4. Centre of mass and centre of gravity coincide in uniform gravitational field

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Correct Option: C
Explanation:

The internal forces all balance each other so that there is no change in the mass distribution of the body, thus center of mass remains unchanged. Rest all options are correct.