Physics JEE Main Centre of Mass | Collision Impulse & Momentum Sample Paper with Answer & Solution 2019
Subtopic of Centre of Mass | Collision | Impulse & Momentum
(1) Electric Potential Difference : Electric Field and the Movement of Charge | Electric Potential | Electric Potential Difference (2) Electric Current : What is an Electric Circuit? | Requirements of a Circuit | Electric Current | Power : Putting Charges to Work | Common Misconceptions Regarding Electric Circuits (3) Electrical Resistance : Journey of a Typical Electron | Resistance | Ohm’s Law | Power Revisited (4) Circuit Connections : Circuit Symbols and Circuit Diagrams | Two Types of Connections | Series Circuits | Parallel Circuits | Combination Circuits
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Collision between two bodies which occurs in a very small interval of time and during which the two bodies exert relatively large forces on each other is called impact. The common normal to the surfaces in contact during the impact is called the line of impact. If centers of mass of the two colliding bodies are located on this line, the impact is a central impact. Otherwise, the impact is said to be eccentric. Our present study will be limited to the central impact of two particles. The analysis of the eccentric impact of two rigid bodies will be considered later.
SYSTEM OF VARIABLE MASS
We recall that all the principles established so for were derived for the systems which neither gain nor lose mass. But there are various situations in which system loses or gains mass during its motion. e.g. in case of Rocket propulsion, its motion depends upon the continued ejection of fuel from it.
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Chapter Exercise Problems
1. When two bodies stick together after collision, the collision is said to be
(a) partially elastic (b) elastic
(c) perfectly inelastic (d) none of the above
2. If momentum is increased by 20%, then K.E. increased by
(a) 44% (b) 55% (c) 66% (d) 77%
3. A bullet is shot from a rifle. As a result the rifle recoils. The kinetic energy of rifle as compared to that of bullet
(a) is less (b) is greater
(c) is equal (d) cannot be concluded
4. A ball hits the floor and rebounds after elastic collision. In this case,
(a) the magnitude of momentum of the ball just after collision is the same as that just before collision
(b) the mechanical energy of ball remains the same in the collision
(c) the total momentum of ball and earth is conserved
(d) the total energy of the ball and earth is conserved
5. In head on elastic collision of two bodies of equal masses
(a) the velocities are interchanged
(b) the momenta are interchanged
(c) the faster body slows down and the slower body speeds up
(d) kinetic energy is conserved
6. Which of the following(s) depend(s) on the choice of the inertial reference frame
(a) Momentum (b) change in momentum (c) Kinetic energy (d) change in kinetic energy
7. A body moving towards a finite body at rest collides with it. It is possible that
(a) both the bodies come to rest
(b) both the bodies move after collision
(c) the moving body comes to rest and the stationary body starts moving
(d) the stationary body remains stationary the moving body changes its velocity
8. After perfectly inelastic collision between two identical particles moving with same speed in different directions the speed of the particles become half the initial speed. The angle between velocities of the two before collision is
(a) 600 (b) 450 (c) 1200 (d) 300
9. A body of mass 2 kg moving with a velocity of 6 m/s strikes inelastically to another body of same mass at rest. The amount of heat evolved during collision is
(a) 36 J (b) 18 J (c) 9 J (d) 3 J
10.. A ball P of mass 2 kg undergoes an elastic collision with another ball Q at rest. After collision, ball P continues to move in its original direction with a speed one-fourth of its original speed. What is the mass of ball Q?
(a) 0.9 kg (b) 1.2 kg (c) 1.5 kg (d) 1.8 kg
11. If two balls each of mass 0.06 kg moving in opposite directions with same speed 4 m/s collide and rebound with the same speed, then the impulse imparted to each ball due to other is
(a) 0.48 kg m/s (b) 0.24 kg m/s (c) 0.81 kg m/s (d) zero
12. A ball approaches a moving wall of infinite mass with speed v along normal to the wall. The speed of the wall is u away from the ball and u < v. The speed of ball after an elastic collision is
(a) u + v away from the wall (b) 2u + v away from the wall
(c) v – u towards from the wall (d) v – 2u away from the wall
13. A sphere collides with another sphere of identical mass kept at rest. After collision, the two spheres move. The collision is perfectly inelastic, then the angle between the directions of motion of the two spheres is
(a) 0° (b) 45° (c) different from 90° (d) 90°
14. A cylindrical solid of mass 10-2 kg and cross-sectional area 10-4 m2 is moving parallel to its axis (the X-axis) with a uniform speed of 103 m/s in the positive direction. At t = 0, its front face passes the plane x = 0. The region to the right of this plane is filled with stationary dust particles of uniform density 10-3 kg/m3. When a dust particle collides with the face of the cylinder, its sticks to its surface. Assuming that the dimensions of the cylinder remain practically unchanged, and that the dust sticks only to the front face of the cylinder, find the x-coordinate of the front of the cylinder at t = 150 s.
15. A cannon of mass M located at the base of an inclined plane shoots a shell of mass m in a horizontal direction with velocity v0. To what vertical height does the cannon ascend the inclined plane as a result of recoil, if the angle of inclination of plane is a and the coefficient of friction between cannon and plane is µ?
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(a) Revise and re-revise. At least 3-4 revisions are a must before you start taking mock tests.
(c) Buy objective books and practice answering questions. Attempt questions one by one and when you are finished, correct your responses.
(d) Test yourself on individual topics. Once you feel you are doing well in a given topic, obtain a sample test for the subject. Evaluate your performance, and continue revising if needed.
(e) Take mock tests (of the same three and a half hour length) one month prior to the test.
(g) Evaluate how many questions you marked incorrectly. Identify problem topics and revise before proceeding to the next chapter or next section.
(h) Do not study the day before the test. What you have studied until then is enough.
(i) Many candidates use coaching centers or private tutors to prepare. You may choose to do so, but before choosing one, identify your needs.
(j) Do not buy too many books. It’s better to read one book 10 times than read 10 books one time.
(k) Sample test questions will give you a feel for what the test looks like. Make sure to go through these before test day.
(l) Stop reading new fundamentals just before the exam. One month before the exam, concentrate on taking mock tests and revise what you have studied.
(m) Have a light snack before leaving for the examination center. This is a must to keep you energized during exam. Keep a water bottle with you during the exam, this will not only help with thirst, but help you to maintain a cool temperament during the examination.
(n) Reach your examination center at least 30-40 minutes in advance to avoid any last minute hassle.
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