CBSE-XI-Physics
09: Centre of Mass, Linear Momentum, Collision
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- #Section : i
- Qstn #1Can the centre of mass of a body be at a point outside the body?Ans : Yes, the centre of mass can be at a point outside the body.
For example, the centre of mass of a ring lies at its centre, which is not a part of the ring.
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- Qstn #2If all the particles of a system lie in X-Y plane, is it necessary that the centre of mass be in X-Y plane?Ans : Yes, if all the particles of a system lie in the X-Y plane, then it's necessary that its centre of mass lies in the X-Y plane.
`` {z}_{\mathit{cm}}=\frac{{m}_{1}{z}_{1}+{m}_{2}{z}_{2}+...{m}_{n}{z}_{n}}{{\displaystyle \underset{}{\sum }}m}``
As all the particles lie in the X-Y plane, their z-coordinates are zero.
Therefore, for the whole system, zcm = 0; i.e., its centre of mass lies in the X-Y plane.
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- Qstn #3If all the particle of a system lie in a cube, is it necessary that the centre of mass be in the cube?Ans : Yes. As a cube is a 3-dimensional body, all the particles of a system lying in a cube lie in the x,y and z plane.
Let the ith element of mass ∆mi is located at the point (xi,yi,zi).
The co-ordinates of the centre of mass are given as:
`` X=\frac{1}{M}{\sum }_{i=1}^{i=n}\left(∆{m}_{i}\right){x}_{i}``
`` Y=\frac{1}{M}{\sum }_{i=1}^{i=n}\left(∆{m}_{i}\right){y}_{i}``
`` Z=\frac{1}{M}{\sum }_{i=1}^{i=n}\left(∆{m}_{i}\right){z}_{i}``
X, Y and Z lie inside the cube because it is a weighted mean.
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- Qstn #4The centre of mass is defined as
R→=1M∑imiri→. Suppose we define “centre of charge” as
R→c=1Q∑iqiri→where qi represents the ith charge placed at
r→iand Q is the total charge of the system.
- #4-aCan the centre of charge of a two-charge system be outside the line segment joining the charges?Ans : Yes
Consider a charge distributed in X-Y plane.
`` {X}_{cm}=\frac{-6q\times 0+q\times 5a}{-6q+q}=-a``
- #4-bIf all the charges of a system are in X-Y plane, is it necessary that the centre of charge be in X-Y plane?Ans : Yes. Because the z-coordinates of all the charges are zero, the centre of charge lies in X-Y plane.
- #4-cIf all the charges of a system lie in a cube, is it necessary that the centre of charge be in the cube?Ans : No, it is not necessary that the centre of charge lies in the cube because charge can be either negative or positive.
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- Qstn #5The weight Mg of an extended body is generally shown in a diagram to act through the centre of mass. Does it mean that the earth does not attract other particles?Ans : In order to simplify the situation, we consider that the weight Mg of an extended body acts through its centre of mass.
Although the earth attracts all the particles, the net effect can be assumed to be at the centre of mass.
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- Qstn #6A bob suspended from the ceiling of a car which is accelerating on a horizontal road. The bob stays at rest with respect to the car with the string making an angle θ with the vertical. The linear momentum of the bob as seen from the road is increasing with time. Is it a violation of conservation of linear momentum? If not, where is the external force changes the linear momentum?Ans : There is no violation of conservation of momentum because in the earth's frame the component of tension is acting in the horizontal direction.
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- Qstn #7You are waiting for a train on a railway platform. Your three-year-old niece is standing on your iron trunk containing the luggage. Why does the trunk not recoil as she jumps off on the platform?Ans : The trunk does not recoil as the girl jumps off on the platform because the force exerted by the girl is less than the limiting friction between the platform and the iron trunk.
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- Qstn #8In a head-on collision between two particles, is it necessary that the particles will acquire a common velocity at least for one instant?Ans : Yes.
For example, consider particle-1 at a velocity of 4 ms-1 and particle-2 at a velocity of 2 ms-1 undergo a head-on collision.
The velocity of particle-1 decreases but particle-2 increases. Therefore, at an instant, their velocities will be equal.
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- Qstn #9A collision experiment is done on a horizontal table kept in an elevator. Do you expect a change in the result if the elevator is accelerated up or down because of the noninertial character of the frame?Ans : No. As the collision experiment is being done on a horizontal table in the elevator that is accelerating up or down in vertical direction, no extra force is experienced in the horizontal direction. Hence, the objects in the horizontal direction remain unaffected.
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- Qstn #10Two bodies make an elastic head-on collision on a smooth horizontal table kept in a car. Do you expect a change in the result if the car is accelerated in a horizontal road because of the non inertial character of the frame? Does the equation “Velocity of separation = Velocity of approach” remain valid in an accelerating car? Does the equation “final momentum = initial momentum” remain valid in the accelerating car?Ans : No, due to the non-inertial character of the frame and the presence of a pseudo force, both the equations, i.e., Velocity of separation = Velocity of approach and Final momentum = Initial momentum, do not remain valid in the accelerating car.
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