NEET-XII-Physics
09: Centre of Mass, Linear Momentum, Collision
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- Qstn #11If the total mechanical energy of a particle is zero, is its linear momentum necessarily zero? Is it necessarily nonzero?Ans : No. As the potential energy can have a negative value, the total energy of the system may sum up to zero.
For example:
Two masses A and B having masses 2 kg and 4 kg respectively move with a velocity of 4 ms-1 in opposite directions.
Kinetic energy of system (A and B)
`` =\frac{1}{2}\times 2\times {4}^{2}+\frac{1}{2}\times 4\times {4}^{2}``
`` =48\,\mathrm{\,J \,}``
If the gravitational potential energy of the system is -48 J, the total energy of the system will be zero. However, the linear momentum will be non-zero.
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- Qstn #12If the linear momentum of a particle is known, can you find its kinetic energy? If the kinetic energy of a particle is know can you find its linear momentum?Ans : Yes, the kinetic energy of the particle can be determined if the value of linear momentum is known.
The kinetic energy is calculated using the formula:
`` \,\mathrm{\,K \,}.\,\mathrm{\,E \,}=\frac{1}{2}m{v}^{2}=\frac{{p}^{2}}{2m}``
`` w\,\mathrm{\,here \,},p\mathit{}\,\mathrm{\,is \,}\,\mathrm{\,the \,}\,\mathrm{\,linear \,}\,\mathrm{\,momemtum \,}\,\mathrm{\,having \,}\,\mathrm{\,value \,}mv.``
But linear momentum cannot be determined even if the kinetic energy is known because linear momentum is a vector quantity, whereas kinetic energy is a scalar quantity. Thus, the direction of the linear momentum remains unknown, however its magnitude can be calculated.
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- Qstn #13What can be said about the centre of mass of a uniform hemisphere without making any calculation? Will its distance from the centre be more than r/2 or less than r/2?Ans : The distance of centre of mass of a uniform hemisphere from its centre will be less than r/2 because the portion of the hemisphere lying below r/2 from the diameter is heavier than the portion lying above r/2.
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- Qstn #14You are holding a cage containing a bird. Do you have to make less effort if the bird flies from its position in the cage and manages to stay in the middle without touching the walls of the cage? Does it makes a difference whether the cage is completely closed or it has rods to let air pass?Ans : More effort is needed when the cage is closed, while less effort is required when the cage has rods to let the air pass. When a bird flies from its position, it pushes the air downwards. Thus, when the bird is in a cage, the net downward force will be equal to the weight of the cage plus the downward force due to air (the weight of the bird).
However, if the cage has rods to let air pass, the downward force exerted by air become less. Therefore, less effort will be required to hold the cage.
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- Qstn #15A fat person is standing on a light plank floating on a calm lake. The person walks from one end to the other on the plank. His friend sitting on the shore watches him and finds that the person hardly moves any distance because the plank moves backward about the same distance as the person moves on the plank. Explain.Ans : According to the question, the weight of plank is very less as compared to the fat person. Therefore, the centre of mass of the whole system effectively lies on the person. As the net external force on the system is zero, the centre of mass of the system does not move.
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- Qstn #16A high-jumper successfully clears the bar. Is it possible that his centre of mass crossed the bar from below it? Try it with appropriate figures.Ans : From the figure, it can be seen that when a high-jumper successfully clears the bar, it is possible that her centre of mass crosses the bar from below it because the legs as well as the arms of the high-jumper are below the bar.
Hence, the point shown in the figure can be her centre of mass.
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- Qstn #17Which of the two persons shown in figure is more likely to fall down? Which external force is responsible for his falling down?
Ans : The person shown on the right hand side of the figure is more likely to fall down because in the given cart frame the pseudo force will be in backward direction.
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- Qstn #18Suppose we define a quantity ‘Linear momentum’ as linear momentum = mass × speed.
The linear momentum of a system of particles is the sum of linear momenta of the individual particles. Can we state principle of conservation of linear momentum as “linear momentum of a system remains constant if no external force acts on it”?Ans : It is not necessary that the linear momentum of a system remains constant even if no external force acts on it because during collision, the sum of magnitudes of momenta does not remain constant.
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- Qstn #19Use the definition of linear momentum from the previous question. Can we state the principle of conservation of linear momentum for a single particle?Ans : Yes, if the external force applied on the particle is zero, its speed does not change and hence, the momentum remains constant.
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- Qstn #20To accelerate a car we ignite petrol in the engine of the car. Since only an external force can accelerate the centre of mass, is it proper to say that “the force generated by the engine accelerates the car”?Ans : Yes, it's proper to say that the force generated by the engine accelerates the car. When petrol burns inside the engine, the piston moves, which in turn rotates the wheel. As the wheel rotates, the frictional forces from the road moves the car.
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- Qstn #21A ball is moved on a horizontal table with some velocity. The ball stops after moving some distance. Which external force is responsible for the change in the momentum of the ball?Ans : The frictional force acting between the surface of the table and the ball is responsible for the change in momentum of the ball. As the force opposes the motion of the ball, it stops after moving some distance.
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- Qstn #22Consider the situation of the previous problem. Take “the table plus the ball” as the system. friction between the table and the ball is then an internal force. As the ball slows down, the momentum of the system decreases. Which external force is responsible for this change in the momentum?Ans : Considering the table plus the ball as a system, it can be said that the frictional force is responsible for the change in the momentum. As the force acts between the surface of the table and ground, it opposes the motion of the table plus the ball. Hence, the ball slows down and the momentum of the system decreases.
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- Qstn #23When a nucleus at rest emits a beta particle, it is found that the velocities of the recoiling nucleus and the beta particle are not along the same straight line. How can this be possible in view of the principle of conservation of momentum?Ans : In view of the principle of conservation of momentum, the given situation is possible because as a beta particle is ejected, another particle called an antineutrino is also ejected.
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- Qstn #24A van is standing on a frictionless portion of a horizontal road. To start the engine, the vehicle must be set in motion in the forward direction. How can be persons sitting inside the van do it without coming out and pushing from behind?Ans : According to the question, the van is standing on a frictionless surface. When throwing something in backward direction, the persons sitting inside the van sets the van in motion in the forward direction according to the principle of conservation of linear momentum.
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- Qstn #25In one-dimensional elastic collision of equal masses, the velocities are interchanged. Can velocities in a one-dimensional collision be interchanged if the masses are not equal?Ans : No. If the masses are different, the velocities in a one-dimensional collision cannot be interchanged because that would be violation of the principle of conservation of momentum.
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