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Two billiard balls A and B. each of mass 50 g and moving in opposite directions with speed of 5 m s-1 each, collide and rebound with the same speed. The impulse imparted to each ball is
- a)0.25 kg m s-1
- b)0.5 kg m s-1
- c)0.1 kg m s-1
- d)0.125 kg m s-1
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Two billiard balls A and B. each of mass 50 g and moving in opposite d...
Initial momentum of ball A = (0.05kg)(5ms(-1)) = 0.25kgms−1
As the speed is reversed on collision,
Final momentum of the ball
A = (0.05kg)(−5ms−1) = −0.25kgms−1
Impulse imparted to the ball A = Change in momentum of ball A
= Final momentum - Initial momentum
= −0.25kg ms−1 −0.25kg ms−1 = −0.5kg ms−1
Similarly,
Initial momentum of ball B = (0.05kg)(−5ms−1) = −0.25kgms−1
Final momentum of ball B = (0.05kg)(5ms−1) = = +0.25kgms−1
Impulse imparted to ball B = (0.25kgms−1) − (−0.25kgms−1) = 0.5kgms−1
Impulse imparted to each ball is 0.5kgms−1 in magnitude. The two impulses are opposite in direction.
Most Upvoted Answer
Two billiard balls A and B. each of mass 50 g and moving in opposite d...
Given information:
- Mass of each billiard ball (A and B): 50 g = 0.05 kg
- Initial speed of each ball: 5 m/s
- After collision, both balls rebound with the same speed.
To find:
The impulse imparted to each ball.
Explanation:
Impulse:
Impulse is the change in momentum of an object and is defined as the product of the force acting on the object and the time interval over which the force acts. Mathematically, impulse is given by:
Impulse = Force × Time
Momentum:
Momentum is the product of mass and velocity of an object. Mathematically, momentum is given by:
Momentum = Mass × Velocity
Conservation of Momentum:
In the absence of external forces, the total momentum of a system of objects remains constant before and after a collision. This is known as the conservation of momentum.
Collision between balls A and B:
Before the collision:
- Mass of ball A = 0.05 kg
- Velocity of ball A = 5 m/s (moving in one direction)
- Mass of ball B = 0.05 kg
- Velocity of ball B = -5 m/s (moving in the opposite direction)
Using the formula for momentum, we can calculate the initial momentum of each ball:
Momentum of ball A = Mass of ball A × Velocity of ball A = 0.05 kg × 5 m/s = 0.25 kg·m/s (in one direction)
Momentum of ball B = Mass of ball B × Velocity of ball B = 0.05 kg × (-5 m/s) = -0.25 kg·m/s (in the opposite direction)
After the collision:
- Both balls rebound with the same speed.
- Let's assume the final velocity of both balls is v (in the opposite direction).
Using the formula for momentum, we can calculate the final momentum of each ball:
Momentum of ball A = Mass of ball A × Velocity of ball A = 0.05 kg × v
Momentum of ball B = Mass of ball B × Velocity of ball B = 0.05 kg × (-v)
According to the conservation of momentum, the total momentum before the collision should be equal to the total momentum after the collision:
Initial momentum of ball A + Initial momentum of ball B = Final momentum of ball A + Final momentum of ball B
0.25 kg·m/s + (-0.25 kg·m/s) = 0.05 kg × v + 0.05 kg × (-v)
0 = v - v
0 = 0
This means that the total momentum before the collision is equal to the total momentum after the collision, which satisfies the conservation of momentum.
Impulse imparted to each ball:
Since the momentum of each ball changes from 0.25 kg·m/s to 0 kg·m/s (reversed direction), the change in momentum (impulse) imparted to each ball is:
Impulse = Final momentum - Initial momentum = 0 kg·m/s - 0.25 kg·m/s = -0.25 kg·m/s
However, impulse is a vector quantity and should have a direction. In this case, the impulse is
- Mass of each billiard ball (A and B): 50 g = 0.05 kg
- Initial speed of each ball: 5 m/s
- After collision, both balls rebound with the same speed.
To find:
The impulse imparted to each ball.
Explanation:
Impulse:
Impulse is the change in momentum of an object and is defined as the product of the force acting on the object and the time interval over which the force acts. Mathematically, impulse is given by:
Impulse = Force × Time
Momentum:
Momentum is the product of mass and velocity of an object. Mathematically, momentum is given by:
Momentum = Mass × Velocity
Conservation of Momentum:
In the absence of external forces, the total momentum of a system of objects remains constant before and after a collision. This is known as the conservation of momentum.
Collision between balls A and B:
Before the collision:
- Mass of ball A = 0.05 kg
- Velocity of ball A = 5 m/s (moving in one direction)
- Mass of ball B = 0.05 kg
- Velocity of ball B = -5 m/s (moving in the opposite direction)
Using the formula for momentum, we can calculate the initial momentum of each ball:
Momentum of ball A = Mass of ball A × Velocity of ball A = 0.05 kg × 5 m/s = 0.25 kg·m/s (in one direction)
Momentum of ball B = Mass of ball B × Velocity of ball B = 0.05 kg × (-5 m/s) = -0.25 kg·m/s (in the opposite direction)
After the collision:
- Both balls rebound with the same speed.
- Let's assume the final velocity of both balls is v (in the opposite direction).
Using the formula for momentum, we can calculate the final momentum of each ball:
Momentum of ball A = Mass of ball A × Velocity of ball A = 0.05 kg × v
Momentum of ball B = Mass of ball B × Velocity of ball B = 0.05 kg × (-v)
According to the conservation of momentum, the total momentum before the collision should be equal to the total momentum after the collision:
Initial momentum of ball A + Initial momentum of ball B = Final momentum of ball A + Final momentum of ball B
0.25 kg·m/s + (-0.25 kg·m/s) = 0.05 kg × v + 0.05 kg × (-v)
0 = v - v
0 = 0
This means that the total momentum before the collision is equal to the total momentum after the collision, which satisfies the conservation of momentum.
Impulse imparted to each ball:
Since the momentum of each ball changes from 0.25 kg·m/s to 0 kg·m/s (reversed direction), the change in momentum (impulse) imparted to each ball is:
Impulse = Final momentum - Initial momentum = 0 kg·m/s - 0.25 kg·m/s = -0.25 kg·m/s
However, impulse is a vector quantity and should have a direction. In this case, the impulse is
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Two billiard balls A and B. each of mass 50 g and moving in opposite directions with speed of 5 m s-1 each, collide and rebound with the same speed. The impulse imparted to each ball isa)0.25 kg m s-1b)0.5 kg m s-1c)0.1kg m s-1d)0.125 kg m s-1Correct answer is option 'B'. Can you explain this answer?
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Two billiard balls A and B. each of mass 50 g and moving in opposite directions with speed of 5 m s-1 each, collide and rebound with the same speed. The impulse imparted to each ball isa)0.25 kg m s-1b)0.5 kg m s-1c)0.1kg m s-1d)0.125 kg m s-1Correct answer is option 'B'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two billiard balls A and B. each of mass 50 g and moving in opposite directions with speed of 5 m s-1 each, collide and rebound with the same speed. The impulse imparted to each ball isa)0.25 kg m s-1b)0.5 kg m s-1c)0.1kg m s-1d)0.125 kg m s-1Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two billiard balls A and B. each of mass 50 g and moving in opposite directions with speed of 5 m s-1 each, collide and rebound with the same speed. The impulse imparted to each ball isa)0.25 kg m s-1b)0.5 kg m s-1c)0.1kg m s-1d)0.125 kg m s-1Correct answer is option 'B'. Can you explain this answer?.
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