Here the tangential acceleration also exits which requires power. Given that $\quad a_{c}=k^{2} r t^{2} \quad$ and &nbsp

Here the tangential acceleration also exits which requires power. Given that $\quad a_{c}=k^{2} r t^{2} \quad$ and $a_{c}=\frac{v^{2}}{r}$ $\frac{v^{2}}{r}=k^{2} r t^{2} 1$ $\mathrm{Or}$ $\mathrm{v}^{2}=\mathrm{k}^{2} \mathrm{r}^{2} \mathrm{t}^{2}$ $\mathrm{v}=\mathrm{krt}$ Tangential acceleration $\quad a=\frac{d v}{d t}=k r$ Now force $F=m a$ $=\mathrm{m} \mathrm{kr}$ So power $\quad P=F \times v$ $\mathrm{P}=(\mathrm{mkr}) \times(\mathrm{krt})$ $P=m k^{2} r^{2} t$

English

5.Work, Energy, Power and Collision

A particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration $ac$ is varying with time t as $a_c = k^2rt^2$ where $k$ is a constant. The power delivered to the particle by the force acting on it

A
$2\pi mk^2r^2$
B
$mk^2r^2t$
C
$\frac{{m{k^4}{r^2}{t^5}}}{3}$
D
Zero

Std 11
Physics

A body of mass $m= 10^{-2} \;kg$ is moving in a medium and experiences a frictional force $F= -kv^2$ Its intial speed is $v_0= 10$ $ms^{-1}$ If, after $10\ s$, its energy is $\frac{1}{8}$ $mv_0^2$ the value of $k$ will be

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A neutron travelling with a velocity $v$ and $K.E.$ $E $ collides perfectly elastically head on with the nucleus of an atom of mass number $A$ at rest. The fraction of total energy retained by neutron is

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Answer the following :

$(a)$ The casing of a rocket in flight burns up due to friction. At whose expense is the heat energy required for burning obtained? The rocket or the atmosphere?

$(b)$ Comets move around the sun in highly elliptical orbits. The gravitational force on the comet due to the sun is not normal to the comet’s velocity in general. Yet the work done by the gravitational force over every complete orbit of the comet is zero. Why ?

$(c)$ An artificial satellite orbiting the earth in very thin atmosphere loses its energy gradually due to dissipation against atmospheric resistance, however small. Why then does its speed increase progressively as it comes closer and closer to the earth ?

$(d)$ In Figure $(i)$ the man walks $2\; m$ carrying a mass of $15\; kg$ on his hands. In Figure $(ii)$, he walks the same distance pulling the rope behind him. The rope goes over a pulley, and a mass of $15\; kg$ hangs at its other end. In which case is the work done greater ?

Medium

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Body $A$ of mass $4m$ moving with speed $u$ collides with another body $B$ of mass $2 m$ at rest the collision is head on and elastic in nature. After the collision the fraction of energy lost by colliding body $A$ is

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A particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration $ac$ is varying with time t as $a_c = k^2rt^2$ where $k$ is a constant. The power delivered to the particle by the force acting on it

Similar Questions

A body of mass $m= 10^{-2} \;kg$ is moving in a medium and experiences a frictional force $F= -kv^2$ Its intial speed is $v_0= 10$ $ms^{-1}$ If, after $10\ s$, its energy is $\frac{1}{8}$ $mv_0^2$ the value of $k$ will be

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Body $A$ of mass $4m$ moving with speed $u$ collides with another body $B$ of mass $2 m$ at rest the collision is head on and elastic in nature. After the collision the fraction of energy lost by colliding body $A$ is