A) \[\frac{1}{2}m{{v}^{2}}\]
B) \[m{{\upsilon }^{2}}\]
C) \[\frac{3}{2}m{{\upsilon }^{2}}\]
D) \[\frac{5}{2}m{{\upsilon }^{2}}\]
Correct Answer: C
Solution :
Total mass = 4m Two pieces, each has mass \[=\text{ }m\] Third piece has a mass \[=4m-m-n\] By law of conservation of momentum \[2m{{\upsilon }_{1}}=m\upsilon \cos {{45}^{o}}+m\upsilon \cos {{45}^{o}}\] \[=\frac{m\upsilon }{\sqrt{2}}+\frac{m\upsilon }{\sqrt{2}}=\frac{2m\upsilon }{\sqrt{2}}\] \[\therefore \] \[{{\upsilon }_{1}}=\frac{\upsilon }{\sqrt{2}}\] Therefore, K.E. \[=\frac{1}{2}m{{\upsilon }^{2}}+\frac{1}{2}m{{\upsilon }^{2}}+\frac{1}{2}2m\upsilon _{1}^{2}\] \[m{{\upsilon }^{2}}+m{{\left( \frac{\upsilon }{\sqrt{2}} \right)}^{2}}=m{{\upsilon }^{2}}+\frac{m{{\upsilon }^{2}}}{2}=\frac{3}{2}m{{\upsilon }^{2}}\]You need to login to perform this action.
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