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Answer:v=41.23 m/s
Explanation:
Given
mass of heavy object
distance of from the axle
mass of rock
Length of rod
distance of from axle
Net torque acting is
Work done by is converted to rock kinetic Energy
thus
Where
Answer:
, assuming that
and
are point charges.
Explanation:
Let denote the coulomb constant. Let
denote the distance between the two point charges. In this question, neither
and
depend on the value of
.
By Coulomb's Law, the magnitude of electrostatic force between and
would be:
.
Find the first and second derivative of with respect to
. (Note that
.)
First derivative:
.
Second derivative:
.
The value of the coulomb constant is greater than
. Thus, the value of the second derivative of
with respect to
would be negative for all real
.
would be convex over all
.
By the convexity of with respect to
, there would be a unique
that globally maximizes
. The first derivative of
with respect to
should be
for that particular
. In other words:
<em>.</em>
.
.
In other words, the force between the two point charges would be maximized when the charge is evenly split:
.