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A nucleus ruptures into two nuclear parts which have their velocity ratio equal to 2:1. What will be the ratio of their nuclear radius
- a)21∕3 : 1
- b)1 : 21∕3
- c)31∕2 : 1
- d)1 : 31∕2
Correct answer is option 'B'. Can you explain this answer?
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A nucleus ruptures into two nuclear parts which have their velocity ra...
Given information:
- Velocity ratio of the two nuclear parts = 2:1
Concept:
- According to the conservation of linear momentum, the total momentum before and after the nuclear rupture remains the same.
Calculation:
- Let the velocities of the two nuclear parts be v1 and v2.
- Given ratio of velocities = 2:1, so v1/v2 = 2/1 = 2
- By conservation of linear momentum, m1v1 = m2v2, where m1 and m2 are the masses of the two nuclear parts.
- Let the radii of the two nuclear parts be r1 and r2.
- Since v1/v2 = 2, we have v1 = 2v2
- Now, the kinetic energy of the two nuclear parts is given by KE = (1/2)mv^2
- We can write KE1 = (1/2)(m1)(2v2)^2 = 4(1/2)(m1)(v2)^2 = 4(1/2)mv2^2 = 4KE2
- As the total kinetic energy before and after the rupture remains the same, KE1 = KE2
- 4KE2 = KE2
- 4(1/2)(m1)(v2)^2 = (1/2)(m2)(v2)^2
- 4m1 = m2
- m1/m2 = 1/4
- (4/3)π(r1)^3/(4/3)π(r2)^3 = 1/4
- r1^3/r2^3 = 1/4
- r1/r2 = 1/2
Therefore, the ratio of the nuclear radii is 1:2, which corresponds to the option 1 : 2.
- Velocity ratio of the two nuclear parts = 2:1
Concept:
- According to the conservation of linear momentum, the total momentum before and after the nuclear rupture remains the same.
Calculation:
- Let the velocities of the two nuclear parts be v1 and v2.
- Given ratio of velocities = 2:1, so v1/v2 = 2/1 = 2
- By conservation of linear momentum, m1v1 = m2v2, where m1 and m2 are the masses of the two nuclear parts.
- Let the radii of the two nuclear parts be r1 and r2.
- Since v1/v2 = 2, we have v1 = 2v2
- Now, the kinetic energy of the two nuclear parts is given by KE = (1/2)mv^2
- We can write KE1 = (1/2)(m1)(2v2)^2 = 4(1/2)(m1)(v2)^2 = 4(1/2)mv2^2 = 4KE2
- As the total kinetic energy before and after the rupture remains the same, KE1 = KE2
- 4KE2 = KE2
- 4(1/2)(m1)(v2)^2 = (1/2)(m2)(v2)^2
- 4m1 = m2
- m1/m2 = 1/4
- (4/3)π(r1)^3/(4/3)π(r2)^3 = 1/4
- r1^3/r2^3 = 1/4
- r1/r2 = 1/2
Therefore, the ratio of the nuclear radii is 1:2, which corresponds to the option 1 : 2.
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A nucleus ruptures into two nuclear parts which have their velocity ratio equal to 2:1. What will be the ratio of their nuclear radiusa)213: 1b)1 : 213c)312 : 1d)1 : 312 Correct answer is option 'B'. Can you explain this answer?
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