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A man of 50 kg mass is standing in a gravity free space at a height of 10 m above the floor. He throws a stone of 0.5 kg mass downwards with a speed 2 m/s. When the stone reaches the floor, the distance of the man above the floor will be:
- a)9.9 m
- b)10.1 m [2010]
- c)10 m
- d)20 m
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A man of 50 kg mass is standing in a gravity free space at a height of...
See as the space is gravity free then there will be no external force so the momentum will be conserved.
So, m1v1=m2v2
50�v1 = 0.5�2
v2 = 1/50
v2 = 0.02m/s
#time taken by stone to reach the ground:
t = s/v
t = 10/2 =5s
#Distance moved by man in 5s:
s = v�t
s = 0.02�5 = 0.1m
Therefore total distance above the ground
=10 + 0.1= 10.1m
So, option B is correct.
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Community Answer
A man of 50 kg mass is standing in a gravity free space at a height of...
Given:
Mass of the man (m1) = 50 kg
Height of the man above the floor (h1) = 10 m
Mass of the stone (m2) = 0.5 kg
Initial velocity of the stone (u) = 2 m/s
To find:
Final distance of the man above the floor (h2)
Concepts used:
1. Conservation of momentum
2. Conservation of gravitational potential energy
Solution:
Step 1: Calculate the velocity of the man before throwing the stone.
Since the man is in a gravity-free space, there is no external force acting on him. Therefore, there is no acceleration and his velocity remains constant.
Using the formula for momentum (p = mv), the initial momentum of the man is:
p1 = m1 * v1
Step 2: Calculate the velocity of the stone when it reaches the floor.
Using the equation of motion (v = u + gt) and substituting u = 2 m/s and g = 9.8 m/s^2, we can find the time taken by the stone to reach the floor:
t = (v - u) / g
Using the formula for momentum, the final momentum of the stone is:
p2 = m2 * v2
Since momentum is conserved, we can equate the initial and final momenta to find the velocity of the man after throwing the stone:
p1 = p2
m1 * v1 = m2 * v2
v2 = (m1 * v1) / m2
Step 3: Calculate the final height of the man above the floor.
The change in gravitational potential energy of the man is equal to the work done against gravity:
ΔPE = m1 * g * (h2 - h1)
Since the stone has been thrown downwards, the change in gravitational potential energy of the stone is equal to the work done by gravity:
ΔPE = -m2 * g * h2
Using the conservation of energy principle, we can equate the changes in gravitational potential energy:
m1 * g * (h2 - h1) = -m2 * g * h2
Simplifying the equation, we get:
h2 = (m1 * h1) / (m1 + m2)
Substituting the given values, we get:
h2 = (50 kg * 10 m) / (50 kg + 0.5 kg)
h2 = 10.1 m
Therefore, the final distance of the man above the floor is 10.1 m, which corresponds to option B.
Mass of the man (m1) = 50 kg
Height of the man above the floor (h1) = 10 m
Mass of the stone (m2) = 0.5 kg
Initial velocity of the stone (u) = 2 m/s
To find:
Final distance of the man above the floor (h2)
Concepts used:
1. Conservation of momentum
2. Conservation of gravitational potential energy
Solution:
Step 1: Calculate the velocity of the man before throwing the stone.
Since the man is in a gravity-free space, there is no external force acting on him. Therefore, there is no acceleration and his velocity remains constant.
Using the formula for momentum (p = mv), the initial momentum of the man is:
p1 = m1 * v1
Step 2: Calculate the velocity of the stone when it reaches the floor.
Using the equation of motion (v = u + gt) and substituting u = 2 m/s and g = 9.8 m/s^2, we can find the time taken by the stone to reach the floor:
t = (v - u) / g
Using the formula for momentum, the final momentum of the stone is:
p2 = m2 * v2
Since momentum is conserved, we can equate the initial and final momenta to find the velocity of the man after throwing the stone:
p1 = p2
m1 * v1 = m2 * v2
v2 = (m1 * v1) / m2
Step 3: Calculate the final height of the man above the floor.
The change in gravitational potential energy of the man is equal to the work done against gravity:
ΔPE = m1 * g * (h2 - h1)
Since the stone has been thrown downwards, the change in gravitational potential energy of the stone is equal to the work done by gravity:
ΔPE = -m2 * g * h2
Using the conservation of energy principle, we can equate the changes in gravitational potential energy:
m1 * g * (h2 - h1) = -m2 * g * h2
Simplifying the equation, we get:
h2 = (m1 * h1) / (m1 + m2)
Substituting the given values, we get:
h2 = (50 kg * 10 m) / (50 kg + 0.5 kg)
h2 = 10.1 m
Therefore, the final distance of the man above the floor is 10.1 m, which corresponds to option B.
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A man of 50 kg mass is standing in a gravity free space at a height of 10 m above the floor. He throws a stone of 0.5 kg mass downwards with a speed 2 m/s. When the stone reaches the floor, the distance of the man above the floor will be:a)9.9 mb)10.1 m [2010]c)10 md)20 mCorrect answer is option 'B'. Can you explain this answer?
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A man of 50 kg mass is standing in a gravity free space at a height of 10 m above the floor. He throws a stone of 0.5 kg mass downwards with a speed 2 m/s. When the stone reaches the floor, the distance of the man above the floor will be:a)9.9 mb)10.1 m [2010]c)10 md)20 mCorrect 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 man of 50 kg mass is standing in a gravity free space at a height of 10 m above the floor. He throws a stone of 0.5 kg mass downwards with a speed 2 m/s. When the stone reaches the floor, the distance of the man above the floor will be:a)9.9 mb)10.1 m [2010]c)10 md)20 mCorrect 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 man of 50 kg mass is standing in a gravity free space at a height of 10 m above the floor. He throws a stone of 0.5 kg mass downwards with a speed 2 m/s. When the stone reaches the floor, the distance of the man above the floor will be:a)9.9 mb)10.1 m [2010]c)10 md)20 mCorrect answer is option 'B'. Can you explain this answer?.
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