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A stone is dropped from a height h. It hits the ground with a certain momentum P. If the same stone is dropped from a height 100% more than the previous height, the momentum when it hits the ground will change by : [2012M]
- a)68%
- b)41%
- c)200%
- d)100%
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A stone is dropped from a height h. It hits the ground with a certain ...
Momentum 
(v2 = u2 + 2gh; Here u = 0)
When stone hits the ground momentum
when same stone dropped from 2h (100% of initial) then momentum
Which is changed by 41% of initial.
Most Upvoted Answer
A stone is dropped from a height h. It hits the ground with a certain ...
Solution:
Given, height of drop = h
Momentum of stone = P
Let's assume the mass of the stone to be 'm' and 'v' be its velocity just before hitting the ground.
Momentum of the stone just before hitting the ground can be given by:
P = mv
When the stone is dropped from a height of h:
Using the principle of conservation of energy, we can write:
mgh = 1/2 mv² + 1/2 Iω²
where,
m = mass of the stone
g = acceleration due to gravity
h = height of drop
v = velocity just before hitting the ground
I = moment of inertia of the stone about its center of mass
ω = angular velocity of the stone just before hitting the ground
Since there is no rotation involved, we can set ω = 0 and simplify the above equation to get:
v = √(2gh)
When the stone is dropped from a height of 2h:
Using the principle of conservation of energy, we can write:
mg(2h) = 1/2 mv² + 1/2 Iω²
where,
m = mass of the stone
g = acceleration due to gravity
2h = height of drop
v = velocity just before hitting the ground
I = moment of inertia of the stone about its center of mass
ω = angular velocity of the stone just before hitting the ground
Since there is no rotation involved, we can set ω = 0 and simplify the above equation to get:
v = √(4gh)
So, the momentum of the stone just before hitting the ground when it is dropped from a height of 2h can be given by:
P' = mv' = m√(4gh)
Now, we can calculate the change in momentum:
ΔP = P' - P = m√(4gh) - mv = mv(√2 - 1)
Percentage change in momentum can be given by:
(ΔP/P) × 100 = [mv(√2 - 1)] / (mv) × 100 = (√2 - 1) × 100 ≈ 41%
Therefore, the percentage change in momentum when the stone is dropped from a height 100% more than the previous height is approximately 41%. Hence, option (b) is the correct answer.
Given, height of drop = h
Momentum of stone = P
Let's assume the mass of the stone to be 'm' and 'v' be its velocity just before hitting the ground.
Momentum of the stone just before hitting the ground can be given by:
P = mv
When the stone is dropped from a height of h:
Using the principle of conservation of energy, we can write:
mgh = 1/2 mv² + 1/2 Iω²
where,
m = mass of the stone
g = acceleration due to gravity
h = height of drop
v = velocity just before hitting the ground
I = moment of inertia of the stone about its center of mass
ω = angular velocity of the stone just before hitting the ground
Since there is no rotation involved, we can set ω = 0 and simplify the above equation to get:
v = √(2gh)
When the stone is dropped from a height of 2h:
Using the principle of conservation of energy, we can write:
mg(2h) = 1/2 mv² + 1/2 Iω²
where,
m = mass of the stone
g = acceleration due to gravity
2h = height of drop
v = velocity just before hitting the ground
I = moment of inertia of the stone about its center of mass
ω = angular velocity of the stone just before hitting the ground
Since there is no rotation involved, we can set ω = 0 and simplify the above equation to get:
v = √(4gh)
So, the momentum of the stone just before hitting the ground when it is dropped from a height of 2h can be given by:
P' = mv' = m√(4gh)
Now, we can calculate the change in momentum:
ΔP = P' - P = m√(4gh) - mv = mv(√2 - 1)
Percentage change in momentum can be given by:
(ΔP/P) × 100 = [mv(√2 - 1)] / (mv) × 100 = (√2 - 1) × 100 ≈ 41%
Therefore, the percentage change in momentum when the stone is dropped from a height 100% more than the previous height is approximately 41%. Hence, option (b) is the correct answer.
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A stone is dropped from a height h. It hits the ground with a certain momentum P. If the same stone is dropped from a height 100% more than the previous height, the momentum when it hits the ground will change by : [2012M]a)68%b)41%c)200%d)100%Correct answer is option 'B'. Can you explain this answer?
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A stone is dropped from a height h. It hits the ground with a certain momentum P. If the same stone is dropped from a height 100% more than the previous height, the momentum when it hits the ground will change by : [2012M]a)68%b)41%c)200%d)100%Correct 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 A stone is dropped from a height h. It hits the ground with a certain momentum P. If the same stone is dropped from a height 100% more than the previous height, the momentum when it hits the ground will change by : [2012M]a)68%b)41%c)200%d)100%Correct 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 A stone is dropped from a height h. It hits the ground with a certain momentum P. If the same stone is dropped from a height 100% more than the previous height, the momentum when it hits the ground will change by : [2012M]a)68%b)41%c)200%d)100%Correct answer is option 'B'. Can you explain this answer?.
A stone is dropped from a height h. It hits the ground with a certain momentum P. If the same stone is dropped from a height 100% more than the previous height, the momentum when it hits the ground will change by : [2012M]a)68%b)41%c)200%d)100%Correct 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 A stone is dropped from a height h. It hits the ground with a certain momentum P. If the same stone is dropped from a height 100% more than the previous height, the momentum when it hits the ground will change by : [2012M]a)68%b)41%c)200%d)100%Correct 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 A stone is dropped from a height h. It hits the ground with a certain momentum P. If the same stone is dropped from a height 100% more than the previous height, the momentum when it hits the ground will change by : [2012M]a)68%b)41%c)200%d)100%Correct answer is option 'B'. Can you explain this answer?.
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