Advertisements
Advertisements
प्रश्न
Two identical ball bearings in contact with each other and resting on a frictionless table are hit head-on by another ball bearing of the same mass moving initially with a speed V. If the collision is elastic, which of the following figure is a possible result after collision?
Advertisements
उत्तर १
Let m be the mass of each ball bearing. Before collision, total K.E. of the system
=1/2mv2 + 0 =1/2 mv2
After collision, K.E. of the system is
Case I, E1 = 1/2 (2m) (v/2)2 = 1/4 mv2
Case II, E2 = 1/2 mv2
Case III, E3 = 1/2(3m) (v/3)2 = 1/6mv2
Thus, case II is the only possibility since K.E. is conserved in this case.
उत्तर २
It can be observed that the total momentum before and after collision in each case is constant.
For an elastic collision, the total kinetic energy of a system remains conserved before and after collision.
For mass of each ball bearing m, we can write:
Total kinetic energy of the system before collision:
= (1/2)mV2 + (1/2)(2m) × 02
= (1/2)mV2
Case (i)
Total kinetic energy of the system after collision:
= (1/2) m × 0 + (1/2) (2m) (V/2)2
= (1/4)mV2
Hence, the kinetic energy of the system is not conserved in case (i).
Case (ii)
Total kinetic energy of the system after collision:
= (1/2)(2m) × 0 + (1/2)mV2
= (1/2) mV2
Hence, the kinetic energy of the system is conserved in case (ii).
Case (iii)
Total kinetic energy of the system after collision:
= (1/2)(3m)(V/3)2
= (1/6)mV2
Hence, the kinetic energy of the system is not conserved in case (iii).
Hence, Case II is the only possibility.
संबंधित प्रश्न
The rate of change of total momentum of a many-particle system is proportional to the ______ on the system.
A molecule in a gas container hits a horizontal wall with speed 200 m s–1 and angle 30° with the normal, and rebounds with the same speed. Is momentum conserved in the collision? Is the collision elastic or inelastic?
The bob A of a pendulum released from 30° to the vertical hits another bob B of the same mass at rest on a table, as shown in the figure. How high does the bob A rise after the collision? Neglect the size of the bobs and assume the collision to be elastic.
Consider the decay of a free neutron at rest : n → p + e–
Show that the two-body decay of this type must necessarily give an electron of fixed energy and, therefore, cannot account for the observed continuous energy distribution in the β-decay of a neutron or a nucleus
Answer the following question.
Discuss the following as special cases of elastic collisions and obtain their exact or approximate final velocities in terms of their initial velocities.
- Colliding bodies are identical.
- A very heavy object collides on a lighter object, initially at rest.
- A very light object collides on a comparatively much massive object, initially at rest.
Solve the following problem.
A spring ball of mass 0.5 kg is dropped from some height. On falling freely for 10 s, it explodes into two fragments of mass ratio 1:2. The lighter fragment continues to travel downwards with a speed of 60 m/s. Calculate the kinetic energy supplied during the explosion.
Define the following:
Coefficient of restitution
Two different unknown masses A and B collide. A is initially at rest when B has a speed v. After collision B has a speed v/2 and moves at right angles to its original direction of motion. Find the direction in which A moves after the collision.
In Rutherford experiment, for head-on collision of a-particles with a gold nucleus, the impact parameter is ______.
A wooden block of mass 'M' moves with velocity 'v ' and collides with another block of mass '4M' which is at rest. After collision, the block of mass 'M' comes to rest. The coefficient of restitution will be ______.
A body of mas 'm' moving with speed 3 m/s collides with a body of mass '2m' at rest. The coalesced mass will start to move with a speed of ______.
During inelastic collision between two bodies, which of the following quantities always remain conserved?
Two pendulums with identical bobs and lengths are suspended from a common support such that in rest position the two bobs are in contact (Figure). One of the bobs is released after being displaced by 10° so that it collides elastically head-on with the other bob.
- Describe the motion of two bobs.
- Draw a graph showing variation in energy of either pendulum with time, for 0 ≤ t ≤ 2T, where T is the period of each pendulum.
A ball of mass 10 kg moving with a velocity of 10`sqrt3` ms–1 along the X-axis, hits another ball of mass 20 kg which is at rest. After collision, the first ball comes to rest and the second one disintegrates into two equal pieces. One of the pieces starts moving along Y-axis at a speed of 10 m/s. The second piece starts moving at a speed of 20 m/s at an angle θ (degree) with respect to the X-axis.
The configuration of pieces after the collision is shown in the figure.
The value of θ to the nearest integer is ______.
A particle of mass m with an initial velocity u`hat"i"` collides perfectly elastically with a mass 3m at rest. It moves with a velocity v`hat"j"` after collision, then, v is given by :
An alpha-particle of mass m suffers 1-dimensional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, 64% of its initial kinetic energy. The mass of the nucleus is ______.
What is a collision?
