NEET Exam > NEET Questions > A body of mass 5 kg explodes at rest into thr...
Start Learning for Free
A body of mass 5 kg explodes at rest into three fragments with masses in the ratio 1 : 1 : 3. The fragements with equal masses fly in mutually perpendicular directions with speeds of 21 m/sec. The velocity of the heaviest fragment will be
- a)11.5 m/sec
- b)14.0 m/sec
- c)7.0 m/sec
- d)9.87 m/sec
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A body of mass 5 kg explodes at rest into three fragments with masses ...
Momentum of first body
p1 = 1 x 21 = 21 kg-m / sec.
Momentum of second body
p2 = 1 x 21 = 21 kg. m / sec.
Momentum of third body p3 = 3V kg - m / sec
Initial momentum = zero
∴ final momentum = 0
p1 = 1 x 21 = 21 kg-m / sec.
Momentum of second body
p2 = 1 x 21 = 21 kg. m / sec.
Momentum of third body p3 = 3V kg - m / sec
Initial momentum = zero
∴ final momentum = 0
Most Upvoted Answer
A body of mass 5 kg explodes at rest into three fragments with masses ...
Given:
- Mass of the body (m) = 5 kg
- Mass ratio of the fragments: 1 : 1 : 3
- Speed of the fragments with equal masses (v) = 21 m/s
To find:
Velocity of the heaviest fragment
Solution:
Step 1: Finding the mass of each fragment
Let the masses of the fragments be m1, m2, and m3.
Given that the mass ratio is 1 : 1 : 3, we can write the equation:
m1 : m2 : m3 = 1 : 1 : 3
Let the common ratio be x, so we can rewrite the equation as:
m1 = x
m2 = x
m3 = 3x
Since the sum of the masses of the fragments must equal the mass of the body, we have:
m1 + m2 + m3 = 5
Substituting the values of m1, m2, and m3, we get:
x + x + 3x = 5
5x = 5
x = 1
Therefore, the masses of the fragments are:
m1 = 1 kg
m2 = 1 kg
m3 = 3 kg
Step 2: Finding the velocity of the heaviest fragment
The fragments with equal masses are flying in mutually perpendicular directions. This means that they form a right-angled triangle, and we can apply the Pythagorean theorem to find the magnitude of their resultant velocity.
Let the magnitude of the resultant velocity be V.
According to the Pythagorean theorem:
V^2 = (v1)^2 + (v2)^2
V^2 = (v)^2 + (v)^2
V^2 = 2v^2
V = sqrt(2v^2)
V = sqrt(2) * v
Since the mass of the third fragment is 3 kg, its velocity will be proportional to the square root of its mass. Therefore, the velocity of the heaviest fragment (V3) will be:
V3 = sqrt(3) * V
Substituting the value of V from above, we get:
V3 = sqrt(3) * sqrt(2) * v
V3 = sqrt(6) * v
Given that v = 21 m/s, we can calculate the velocity of the heaviest fragment:
V3 = sqrt(6) * 21
V3 ≈ 9.87 m/s
Therefore, the correct answer is option D) 9.87 m/s.
- Mass of the body (m) = 5 kg
- Mass ratio of the fragments: 1 : 1 : 3
- Speed of the fragments with equal masses (v) = 21 m/s
To find:
Velocity of the heaviest fragment
Solution:
Step 1: Finding the mass of each fragment
Let the masses of the fragments be m1, m2, and m3.
Given that the mass ratio is 1 : 1 : 3, we can write the equation:
m1 : m2 : m3 = 1 : 1 : 3
Let the common ratio be x, so we can rewrite the equation as:
m1 = x
m2 = x
m3 = 3x
Since the sum of the masses of the fragments must equal the mass of the body, we have:
m1 + m2 + m3 = 5
Substituting the values of m1, m2, and m3, we get:
x + x + 3x = 5
5x = 5
x = 1
Therefore, the masses of the fragments are:
m1 = 1 kg
m2 = 1 kg
m3 = 3 kg
Step 2: Finding the velocity of the heaviest fragment
The fragments with equal masses are flying in mutually perpendicular directions. This means that they form a right-angled triangle, and we can apply the Pythagorean theorem to find the magnitude of their resultant velocity.
Let the magnitude of the resultant velocity be V.
According to the Pythagorean theorem:
V^2 = (v1)^2 + (v2)^2
V^2 = (v)^2 + (v)^2
V^2 = 2v^2
V = sqrt(2v^2)
V = sqrt(2) * v
Since the mass of the third fragment is 3 kg, its velocity will be proportional to the square root of its mass. Therefore, the velocity of the heaviest fragment (V3) will be:
V3 = sqrt(3) * V
Substituting the value of V from above, we get:
V3 = sqrt(3) * sqrt(2) * v
V3 = sqrt(6) * v
Given that v = 21 m/s, we can calculate the velocity of the heaviest fragment:
V3 = sqrt(6) * 21
V3 ≈ 9.87 m/s
Therefore, the correct answer is option D) 9.87 m/s.
Attention NEET Students!
To make sure you are not studying endlessly, EduRev has designed NEET study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in NEET.
|
Explore Courses for NEET exam
|
|
Similar NEET Doubts
Top Courses for NEETView all
A body of mass 5 kg explodes at rest into three fragments with masses in the ratio 1 : 1 : 3. The fragements with equal masses fly in mutually perpendicular directions with speeds of 21 m/sec. The velocity of the heaviest fragment will bea)11.5 m/secb)14.0 m/secc)7.0 m/secd)9.87 m/secCorrect answer is option 'D'. Can you explain this answer?
Question Description
A body of mass 5 kg explodes at rest into three fragments with masses in the ratio 1 : 1 : 3. The fragements with equal masses fly in mutually perpendicular directions with speeds of 21 m/sec. The velocity of the heaviest fragment will bea)11.5 m/secb)14.0 m/secc)7.0 m/secd)9.87 m/secCorrect answer is option 'D'. 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 body of mass 5 kg explodes at rest into three fragments with masses in the ratio 1 : 1 : 3. The fragements with equal masses fly in mutually perpendicular directions with speeds of 21 m/sec. The velocity of the heaviest fragment will bea)11.5 m/secb)14.0 m/secc)7.0 m/secd)9.87 m/secCorrect answer is option 'D'. 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 body of mass 5 kg explodes at rest into three fragments with masses in the ratio 1 : 1 : 3. The fragements with equal masses fly in mutually perpendicular directions with speeds of 21 m/sec. The velocity of the heaviest fragment will bea)11.5 m/secb)14.0 m/secc)7.0 m/secd)9.87 m/secCorrect answer is option 'D'. Can you explain this answer?.
A body of mass 5 kg explodes at rest into three fragments with masses in the ratio 1 : 1 : 3. The fragements with equal masses fly in mutually perpendicular directions with speeds of 21 m/sec. The velocity of the heaviest fragment will bea)11.5 m/secb)14.0 m/secc)7.0 m/secd)9.87 m/secCorrect answer is option 'D'. 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 body of mass 5 kg explodes at rest into three fragments with masses in the ratio 1 : 1 : 3. The fragements with equal masses fly in mutually perpendicular directions with speeds of 21 m/sec. The velocity of the heaviest fragment will bea)11.5 m/secb)14.0 m/secc)7.0 m/secd)9.87 m/secCorrect answer is option 'D'. 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 body of mass 5 kg explodes at rest into three fragments with masses in the ratio 1 : 1 : 3. The fragements with equal masses fly in mutually perpendicular directions with speeds of 21 m/sec. The velocity of the heaviest fragment will bea)11.5 m/secb)14.0 m/secc)7.0 m/secd)9.87 m/secCorrect answer is option 'D'. Can you explain this answer?.
Solutions for A body of mass 5 kg explodes at rest into three fragments with masses in the ratio 1 : 1 : 3. The fragements with equal masses fly in mutually perpendicular directions with speeds of 21 m/sec. The velocity of the heaviest fragment will bea)11.5 m/secb)14.0 m/secc)7.0 m/secd)9.87 m/secCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for NEET.
Download more important topics, notes, lectures and mock test series for NEET Exam by signing up for free.
Here you can find the meaning of A body of mass 5 kg explodes at rest into three fragments with masses in the ratio 1 : 1 : 3. The fragements with equal masses fly in mutually perpendicular directions with speeds of 21 m/sec. The velocity of the heaviest fragment will bea)11.5 m/secb)14.0 m/secc)7.0 m/secd)9.87 m/secCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A body of mass 5 kg explodes at rest into three fragments with masses in the ratio 1 : 1 : 3. The fragements with equal masses fly in mutually perpendicular directions with speeds of 21 m/sec. The velocity of the heaviest fragment will bea)11.5 m/secb)14.0 m/secc)7.0 m/secd)9.87 m/secCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for A body of mass 5 kg explodes at rest into three fragments with masses in the ratio 1 : 1 : 3. The fragements with equal masses fly in mutually perpendicular directions with speeds of 21 m/sec. The velocity of the heaviest fragment will bea)11.5 m/secb)14.0 m/secc)7.0 m/secd)9.87 m/secCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of A body of mass 5 kg explodes at rest into three fragments with masses in the ratio 1 : 1 : 3. The fragements with equal masses fly in mutually perpendicular directions with speeds of 21 m/sec. The velocity of the heaviest fragment will bea)11.5 m/secb)14.0 m/secc)7.0 m/secd)9.87 m/secCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A body of mass 5 kg explodes at rest into three fragments with masses in the ratio 1 : 1 : 3. The fragements with equal masses fly in mutually perpendicular directions with speeds of 21 m/sec. The velocity of the heaviest fragment will bea)11.5 m/secb)14.0 m/secc)7.0 m/secd)9.87 m/secCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice NEET tests.
|
|
Explore Courses for NEET exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup