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At high altitude, a body explodes at rest into two equal fragments with one fragment receiving horizontal velocity of 10 m/s. Time taken by the two radius vectors connecting point of explosion to fragment to make 90° is (g = 10 m/s2)
- a)10 s
- b)4 s
- c)2 s
- d)1 s
Correct answer is option 'C'. Can you explain this answer?
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At high altitude, a body explodes at rest into two equal fragments wit...
To solve this problem, we can use the conservation of momentum.
Let's assume the mass of the body before the explosion is m, and the mass of each fragment after the explosion is m/2.
Since the body is at rest before the explosion, its initial momentum is zero. After the explosion, the momentum of the two fragments must add up to zero to conserve momentum.
Let v1 be the velocity of the first fragment after the explosion, and v2 be the velocity of the second fragment after the explosion. We are given that v1 = 10 m/s.
Using the conservation of momentum, we can write the equation:
(m/2)(v1) + (m/2)(v2) = 0
Simplifying the equation, we get:
v2 = -v1
Since the magnitude of v1 is 10 m/s, the magnitude of v2 is also 10 m/s.
Now, let's consider the two radius vectors connecting the point of explosion to each fragment. Let's call these vectors r1 and r2.
Since the fragments have equal masses, the magnitudes of r1 and r2 are the same. Let's call this magnitude r.
We are asked to find the time taken by the two radius vectors to make a 90-degree angle with each other.
The angle between two vectors can be found using the dot product:
r1 · r2 = |r1| |r2| cosθ
Since r1 and r2 are perpendicular, cosθ = 0.
Therefore, r1 · r2 = 0
The dot product of two vectors is given by the product of their magnitudes and the cosine of the angle between them.
|r1| |r2| cosθ = 0
Since |r1| = |r2| = r, we have:
r^2 cosθ = 0
Since cosθ = 0, the equation becomes:
r^2 * 0 = 0
This equation holds true for any value of r. Therefore, there is no unique value for the time taken by the two radius vectors to make a 90-degree angle with each other.
Let's assume the mass of the body before the explosion is m, and the mass of each fragment after the explosion is m/2.
Since the body is at rest before the explosion, its initial momentum is zero. After the explosion, the momentum of the two fragments must add up to zero to conserve momentum.
Let v1 be the velocity of the first fragment after the explosion, and v2 be the velocity of the second fragment after the explosion. We are given that v1 = 10 m/s.
Using the conservation of momentum, we can write the equation:
(m/2)(v1) + (m/2)(v2) = 0
Simplifying the equation, we get:
v2 = -v1
Since the magnitude of v1 is 10 m/s, the magnitude of v2 is also 10 m/s.
Now, let's consider the two radius vectors connecting the point of explosion to each fragment. Let's call these vectors r1 and r2.
Since the fragments have equal masses, the magnitudes of r1 and r2 are the same. Let's call this magnitude r.
We are asked to find the time taken by the two radius vectors to make a 90-degree angle with each other.
The angle between two vectors can be found using the dot product:
r1 · r2 = |r1| |r2| cosθ
Since r1 and r2 are perpendicular, cosθ = 0.
Therefore, r1 · r2 = 0
The dot product of two vectors is given by the product of their magnitudes and the cosine of the angle between them.
|r1| |r2| cosθ = 0
Since |r1| = |r2| = r, we have:
r^2 cosθ = 0
Since cosθ = 0, the equation becomes:
r^2 * 0 = 0
This equation holds true for any value of r. Therefore, there is no unique value for the time taken by the two radius vectors to make a 90-degree angle with each other.
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At high altitude, a body explodes at rest into two equal fragments with one fragment receiving horizontal velocity of 10 m/s. Time taken by the two radius vectors connecting point of explosion to fragment to make 90° is (g = 10 m/s2)a)10 sb)4 sc)2 sd)1 sCorrect answer is option 'C'. Can you explain this answer?
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At high altitude, a body explodes at rest into two equal fragments with one fragment receiving horizontal velocity of 10 m/s. Time taken by the two radius vectors connecting point of explosion to fragment to make 90° is (g = 10 m/s2)a)10 sb)4 sc)2 sd)1 sCorrect answer is option 'C'. 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 At high altitude, a body explodes at rest into two equal fragments with one fragment receiving horizontal velocity of 10 m/s. Time taken by the two radius vectors connecting point of explosion to fragment to make 90° is (g = 10 m/s2)a)10 sb)4 sc)2 sd)1 sCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At high altitude, a body explodes at rest into two equal fragments with one fragment receiving horizontal velocity of 10 m/s. Time taken by the two radius vectors connecting point of explosion to fragment to make 90° is (g = 10 m/s2)a)10 sb)4 sc)2 sd)1 sCorrect answer is option 'C'. Can you explain this answer?.
At high altitude, a body explodes at rest into two equal fragments with one fragment receiving horizontal velocity of 10 m/s. Time taken by the two radius vectors connecting point of explosion to fragment to make 90° is (g = 10 m/s2)a)10 sb)4 sc)2 sd)1 sCorrect answer is option 'C'. 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 At high altitude, a body explodes at rest into two equal fragments with one fragment receiving horizontal velocity of 10 m/s. Time taken by the two radius vectors connecting point of explosion to fragment to make 90° is (g = 10 m/s2)a)10 sb)4 sc)2 sd)1 sCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At high altitude, a body explodes at rest into two equal fragments with one fragment receiving horizontal velocity of 10 m/s. Time taken by the two radius vectors connecting point of explosion to fragment to make 90° is (g = 10 m/s2)a)10 sb)4 sc)2 sd)1 sCorrect answer is option 'C'. Can you explain this answer?.
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