A particle moves in 
plane under the influence of a force 
such that its linear momentum is 
. If k is constant, the angle between 
and 
will be:
Text Solution
Verified by ExpertsA
To find the angle between 
and 
, we first need to understand the relationship between force and momentum. The force 
acting on a particle is related to the rate of change of its linear momentum 
with respect to time, as described by Newton's second law of motion:
Given the expression for the momentum 
, we can find 
by differentiating 
with respect to 
:
So, 
.
Now, to find the angle between 
and 
, we use the dot product formula:
where 
is the angle between 
and 
. However, in this case, it's more insightful to see if 
and 
are orthogonal (at a 
angle to each other), because the dot product of two perpendicular vectors is zero.
The dot product of 
and 
is:
The result is zero, indicating that the angle between 
and 
is indeed 
.
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