If 
and 
represent the angular momentum and linear momentum respectively of a particle of mass ' 
' having position vector as 
. The direction of force is
Text Solution
Verified by ExpertsC
Let's analyze the situation step by step.
The particle's position vector is given by
,
which represents uniform circular motion in the xy-plane.
Its velocity is the time derivative of the position:
.
The acceleration, obtained by differentiating the velocity, is:
Notice that this can be rewritten as:
This indicates that the acceleration (and hence the force, since 
) is directed opposite to the position vector 
-that is, radially inward.
To check against the given options: Option A (Opposite to 
): The angular momentum 
is perpendicular to the plane of motion (along 
) and does not indicate a direction in the plane.
Option B (Opposite to 
): For a particle in circular motion, when you compute 
(with 
), you'll find that it is proportional to 
. Thus, the direction opposite to 
would be the same as 
, which is the outward radial direction-not matching the inward (centripetal) force.
Option D (Opposite to 
): The linear momentum is tangential; the force (centripetal) is not tangential but directed radially inward. Option C (Opposite to 
): As we found, the acceleration (and hence force) is given by 
, which is clearly opposite to 
.
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems