| Three blocks A, B and C are lying on a smooth horizontal surface, as shown in the figure. A and B have equal masses, m while C has mass M. Block A is given an initial speed v towards B due to which it collides with B perfectly inelastically \[\frac{5}{6}th\] of the initial kinetic energy is lost in whole process. What is value of M/m? [JEE Main 09-Jan-2019 Morning] |
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A) 2
B) 3
C) 5
D) 4
Correct Answer: D
Solution :
| [d] |
| \[\frac{{{P}^{2}}}{2m}\,\,-\,\,\frac{{{P}^{2}}}{2(2m+M)}\,\,=\,\,\frac{5}{6}\,\,\frac{{{P}^{2}}}{2m}\] |
| \[\frac{1}{m}\,\,-\,\,\frac{1}{(2m+M)}\,\,=\,\,\,\frac{5}{6\,m}\] |
| \[\frac{2m+M-m}{m(2m+M)}\,\,=\,\,\,\frac{5}{6\,m}\] |
| \[6\left( m+M \right)=5\left( 2m+M \right)\] |
| \[6m+6M=10m+5M\] |
| \[4m=M\] |
| \[\frac{m}{M}\,\,=\,\,\frac{1}{4}\] |
| \[\Rightarrow \,\,\frac{M}{m}\,\,=\,\,4\] |
| Option [d] is correct. |
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