51.
1
Two point masses 1 and 2 move with uniform velocities
v, and v2, respectively. Their initial position vectors are
Fi and 7z , respectively. Which of the following should be
satisfied for the collision of the point masses?
Answers
Correct Question:-
Two point masses 1 and 2 move with uniform velocities and respectively. Their initial position vectors are and respectively. What is the condition for the two point masses to collide with each other?
Solution:-
Let the point masses collide each other after seconds of the beginning of their journey (assume they start to move simultaneously).
So the displacements of the two point masses are and respectively.
As in the fig., the particles attain same position vector during collision, which is given by,
Also,
Thus, from (1) and (2),
Since is scalar, we can take magnitude only in RHS of (3) as,
From (3) and (4),
By rule of alternendo,
This means, the unit vector along the relative position vector of the two point masses should be equal to the negative unit vector along the relative velocity vector.