A particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration ${a_c}$ is varying with time t as, ${a_c} = {k^2}r{t^2}$, The power delivered to the particle by the forces acting on it is
A particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration ${a_c}$ is varying with time t as, ${a_c} = {k^2}r{t^2}$, The power delivered to the particle by the forces acting on it is
$2\pi m{k^2}{r^2}t$
$m{k^2}{r^2}t$
$\frac{{m{k^4}{r^2}{t^5}}}{3}$
Zero
A particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration ${a_c}$ is varying with time t as, ${a_c} = {k^2}r{t^2}$, The power delivered to the particle by the forces acting on it is
Here the tangential acceleration also exits which requires power.
Given that ${a_C} = {k^2}r{t^2}$ and ${a_C} = \frac{{{v^2}}}{r}$
$\frac{{{v^2}}}{r} = {k^2}r{t^2}$
or ${v^2} = {k^2}{r^2}{t^2}$ or $v = krt$
Tangential acceleration $a = \frac{{dv}}{{dt}} = kr$
Now force $F = m \times a = mkr$
So power $P = F \times v = mkr \times krt = m{k^2}{r^2}t$
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