question_answer

Two point masses 1 and 2 move with uniform velocities \[\Delta ABC,\left| \begin{matrix}    1 & a & b  \\    1 & c & a  \\    1 & b & c  \\ \end{matrix} \right|=0,\] and \[{{\sin }^{2}}A+{{\sin }^{2}}B\text{ }+{{\sin }^{2}}C\] respectively. Their initial position vectors are \[\frac{3\sqrt{3}}{2}\] and \[\frac{9}{4}\] respectively. Which of the following should be satisfied for the collision of the point masses?

A) \[\frac{5}{4}\]   

B) \[y=x,x=e,y=\frac{1}{x}\]

C) \[\frac{1}{2}\]   

D) \[\frac{3}{2}\]

Correct Answer: A

Solution :

For collision,       \[({{\mu }_{s}}=1.4)\] \[\frac{2}{\sqrt{3}}\left( \frac{\tau }{Bi} \right)\]                               \[2{{\left( \frac{\tau }{\sqrt{3}Bi} \right)}^{1/2}}\] Equating unit vectors, we get \[\frac{2}{\sqrt{3}}{{\left( \frac{\tau }{Bi} \right)}^{1/2}}\]