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In a Head-on Collision Between Two Particles, is It Necessary that the Particles Will Acquire a Common Velocity at Least for One Instant? - Physics

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प्रश्न

In a head-on collision between two particles, is it necessary that the particles will acquire a common velocity at least for one instant?

टीपा लिहा

उत्तर

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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पाठ 9: Centre of Mass, Linear Momentum, Collision - Short Answers [पृष्ठ १५६]

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एचसी वर्मा Concepts of Physics Vol. 1 [English] Class 11 and 12
पाठ 9 Centre of Mass, Linear Momentum, Collision
Short Answers | Q 8 | पृष्ठ १५६

संबंधित प्रश्‍न

Consider the following the equations
(A) \[\vec{R} = \frac{1}{M} \sum_i m_i \vec{r_i}\] and
(B) \[\vec{a}_{CM} = \frac{\vec{F}}{M}\] 
In a noninertial frame


The centre of mass of a system of particles is at the origin. It follows that


Find the centre of mass of a uniform plate having semicircular inner and outer boundaries of radii R1 and R2.


Two persons each of mass m are standing at the two extremes of a railroad car of mass M resting on a smooth track(In the following figure). The person on left jumps to the left with a horizontal speed u with respect to the state of the car before the jump. Thereafter, the other person jumps to the right, again with the same horizontal speed u with respect to the state of the car before his jump. Find the velocity of the car after both the persons have jumped off. 


Two balls having masses m and 2m are fastened to two light strings of same length l (See figure). The other ends of the strings are fixed at O. The strings are kept in the same horizontal line and the system is released from rest. The collision between the balls is elastic. (a) Find the velocity of the balls just after their collision. (b) How high will the ball rise after the collision?


Two small balls A and B, each of mass m, are joined rigidly to the ends of a light rod of length L (see the following figure). The system translates on a frictionless horizontal surface with a velocity \[\nu_0\] in a direction perpendicular to the rod. A particle P of mass m kept at rest on the surface sticks to the ball A as the ball collides with it. Find
(a) the linear speeds of the balls A and B after the collision, (b) the velocity of the centre of mass C of the system A + B + P and (c) the angular speed of the system about C after the collision.

[Hint : The light rod will exert a force on the ball B
only along its length.]


The centre of mass of a system of particles does not depend upon, ______


Define centre of mass.


Find out the centre of mass for the given geometrical structures.

a) Equilateral triangle

b) Cylinder

c) Square


In system of two particles of masses 'm1' and 'm2', the first particle is moved by a distance 'd' towards the centre of mass. To keep the centre of mass unchanged, the second particle will have to be moved by a distance ______.


The centre of mass of a system of two particles divides the distance between them ______.


The radius and mass of earth are increased by 0.5%. Which of the following statements are true at the surface of the earth?


A mass of 1kg is suspended by a string. It is first lifted up with an acceleration of 4.9 m/s2 and then lowered down with same acceleration. The ratio of tensions in the string in the two cases, respectively is g = 9.8 m/s2 ______.


The ratio of weights of a man inside a lift when it is stationary and when it is going down with a uniform acceleration 'a' is 3 : 2. The value of 'a' will be ______.

(a< g, g = acceleration due to gravity)


A uniform square plate has a small piece Q of an irregular shape removed and glued to the centre of the plate leaving a hole behind figure. The CM of the plate is now in the following quadrant of x-y plane ______.


Find the centre of mass of a uniform (a) half-disc, (b) quarter-disc.


A uniform square plate S (side c) and a uniform rectangular plate R (sides b, a) have identical areas and masses (Figure).


Show that

  1. IxR/IxS < 1
  2. IyR/IyS > 1
  3. IzR/IzS > 1

The mass per unit length of a non-uniform rod of length L varies as m = λx where λ is constant. The centre of mass of the rod will be at ______.


The spheres of masses 2 kg and 4 kg are situated at the opposite ends of wooden bars of length 9 m. Where does the centre of mass of the system will ______.


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