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n small balls each of mass m impinge elastically each second on a surface with velocity u. The force experienced by the surface will be
- a)mnu
- b)2 mnu
- c)4 mnu
- d)1/2 mnu
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
n small balls each of mass m impinge elastically each second on a surf...
The Force experienced by the surface is nothing but impulse received by it.both intial and final direction of velocities are opposite then impulse received is mnu-(- mnu-).so it is equal to 2mnu.
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n small balls each of mass m impinge elastically each second on a surf...
Explanation:
When n small balls each of mass m impinge elastically on a surface with velocity u, the force experienced by the surface can be calculated using the principles of momentum and Newton's third law of motion.
Momentum:
The momentum of an object is the product of its mass and velocity. In this case, each ball has a mass m and a velocity u, so the momentum of each ball is given by:
Momentum = mass x velocity
= m x u
Since there are n balls, the total momentum is given by:
Total momentum = n x (m x u)
= nmu
Newton's Third Law of Motion:
According to Newton's third law of motion, for every action, there is an equal and opposite reaction. When a ball impinges on the surface, it exerts a force on the surface, and the surface exerts an equal and opposite force on the ball.
Therefore, the force experienced by the surface due to each ball is equal to the rate of change of momentum of the ball. Since the balls impinge on the surface elastically, the change in momentum is equal to twice the momentum of each ball. Hence, the force experienced by the surface due to each ball is given by:
Force = 2 x momentum
= 2 x nmu
= 2nmu
Total Force:
Since there are n balls impinging on the surface per second, the total force experienced by the surface per second is given by:
Total force = n x (2nmu)
= 2n^2mu
Comparing this with the given options, we can see that the correct answer is option B: 2mn^2u.
When n small balls each of mass m impinge elastically on a surface with velocity u, the force experienced by the surface can be calculated using the principles of momentum and Newton's third law of motion.
Momentum:
The momentum of an object is the product of its mass and velocity. In this case, each ball has a mass m and a velocity u, so the momentum of each ball is given by:
Momentum = mass x velocity
= m x u
Since there are n balls, the total momentum is given by:
Total momentum = n x (m x u)
= nmu
Newton's Third Law of Motion:
According to Newton's third law of motion, for every action, there is an equal and opposite reaction. When a ball impinges on the surface, it exerts a force on the surface, and the surface exerts an equal and opposite force on the ball.
Therefore, the force experienced by the surface due to each ball is equal to the rate of change of momentum of the ball. Since the balls impinge on the surface elastically, the change in momentum is equal to twice the momentum of each ball. Hence, the force experienced by the surface due to each ball is given by:
Force = 2 x momentum
= 2 x nmu
= 2nmu
Total Force:
Since there are n balls impinging on the surface per second, the total force experienced by the surface per second is given by:
Total force = n x (2nmu)
= 2n^2mu
Comparing this with the given options, we can see that the correct answer is option B: 2mn^2u.
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n small balls each of mass m impinge elastically each second on a surface with velocity u. The force experienced by the surface will bea)mnub)2 mnuc)4 mnud)1/2 mnuCorrect answer is option 'B'. Can you explain this answer?
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