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A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is 1: 21/3 Their respective speed have a ratio of n : 1. The value of n is __________.
Correct answer is '2'. Can you explain this answer?
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A nucleus disintegrates into two nuclear parts, in such a way that rat...
Given information:
A nucleus disintegrates into two nuclear parts.
Ratio of their nuclear sizes is 1: 2^(1/3).
Ratio of their speeds is n: 1.
To find:
The value of n.
Solution:
Let the nuclear size of the first part be x.
Then, the nuclear size of the second part will be 2^(1/3)x.
The ratio of their speeds is n: 1.
We know that the ratio of speeds is inversely proportional to the ratio of nuclear sizes. Therefore,
nuclear size of the first part / nuclear size of the second part = 1/n
x / (2^(1/3)x) = 1/n
Simplifying the above equation, we get:
1 / (2^(1/3)) = 1/n
To solve for n, we need to find the value of 1 / (2^(1/3)).
Calculating the value of 1 / (2^(1/3)):
Let's first simplify 2^(1/3).
2^(1/3) can be written as (2^(1/3))^3 = 2.
Therefore, 1 / (2^(1/3)) = 1 / 2 = 0.5.
Substituting the value of 1 / (2^(1/3)) in the equation:
0.5 = 1/n
Solving for n, we get:
n = 1 / 0.5
n = 2
Hence, the value of n is 2.
A nucleus disintegrates into two nuclear parts.
Ratio of their nuclear sizes is 1: 2^(1/3).
Ratio of their speeds is n: 1.
To find:
The value of n.
Solution:
Let the nuclear size of the first part be x.
Then, the nuclear size of the second part will be 2^(1/3)x.
The ratio of their speeds is n: 1.
We know that the ratio of speeds is inversely proportional to the ratio of nuclear sizes. Therefore,
nuclear size of the first part / nuclear size of the second part = 1/n
x / (2^(1/3)x) = 1/n
Simplifying the above equation, we get:
1 / (2^(1/3)) = 1/n
To solve for n, we need to find the value of 1 / (2^(1/3)).
Calculating the value of 1 / (2^(1/3)):
Let's first simplify 2^(1/3).
2^(1/3) can be written as (2^(1/3))^3 = 2.
Therefore, 1 / (2^(1/3)) = 1 / 2 = 0.5.
Substituting the value of 1 / (2^(1/3)) in the equation:
0.5 = 1/n
Solving for n, we get:
n = 1 / 0.5
n = 2
Hence, the value of n is 2.
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Community Answer
A nucleus disintegrates into two nuclear parts, in such a way that rat...
Let the masses of the two nuclear parts be m1 and m2 and their respective speeds be v1 and v2.
According to the problem, the ratio of their nuclear sizes is 1 : 21/3. Since the nuclear size is proportional to the cube root of the mass, we can write:
Now, according to the conservation of linear momentum, the momentum before disintegration is equal to the momentum after disintegration:
From the problem statement, the ratio of their respective speeds is n : 1, so we can write:
Substitute the expression for v1 into the momentum conservation equation:
We know the mass ratio, so substitute that into the equation:
Divide both sides by
Now, solve for n:
n = 2
Thus, the value of n is 2.
According to the problem, the ratio of their nuclear sizes is 1 : 21/3. Since the nuclear size is proportional to the cube root of the mass, we can write:
Now, according to the conservation of linear momentum, the momentum before disintegration is equal to the momentum after disintegration:
From the problem statement, the ratio of their respective speeds is n : 1, so we can write:
Substitute the expression for v1 into the momentum conservation equation:
We know the mass ratio, so substitute that into the equation:
Divide both sides by
Now, solve for n:
n = 2
Thus, the value of n is 2.
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A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is 1: 21/3Their respective speed have a ratio of n : 1.The value of n is __________.Correct answer is '2'. Can you explain this answer?
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A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is 1: 21/3Their respective speed have a ratio of n : 1.The value of n is __________.Correct answer is '2'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is 1: 21/3Their respective speed have a ratio of n : 1.The value of n is __________.Correct answer is '2'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is 1: 21/3Their respective speed have a ratio of n : 1.The value of n is __________.Correct answer is '2'. Can you explain this answer?.
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