question_answer

A particle of mass m moves in the XY plane with a velocity v along the straight line AB. If the angular momentum of the particle with respect to origin o is \[\rho \] when it is at A and \[\lambda \] when it is at B, then

A) \[\frac{\sigma }{\rho \lambda }\]

B)                       \[\frac{\rho }{\sigma \lambda }\]

C)  the relationship between \[\frac{\lambda }{\sigma \rho }\] and \[\rho \lambda \sigma \] depends upon the slope of the line AS

D) \[({{T}_{i}})\]

Correct Answer: B

Solution :

From the definition of angular momentum, \[{{v}_{i}}\] Therefore, the magnitude of L is \[{{v}_{f}}({{R}_{e}}\] where \[{{M}_{e}}\] is the distance of closest approach of the particle to the origin. As d is same for both the particles, hence \[v_{f}^{2}=v_{i}^{2}+\frac{2Gm}{{{M}_{e}}R}\left( 1-\frac{1}{10} \right)\]