(B) The centripetal acceleration is given by $a_c = \frac{v^2}{r} = k^2rt^2$.From this,we find the speed $v$ of the particle: $v^2 = k^2r^2t^2$,which

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(B) The centripetal acceleration is given by $a_c = \frac{v^2}{r} = k^2rt^2$.From this,we find the speed $v$ of the particle: $v^2 = k^2r^2t^2$,which implies $v = krt$.The tangential acceleration $a_t$ is the rate of change of speed: $a_t = \frac{dv}{dt} = \frac{d}{dt}(krt) = kr$.The tangential force acting on the particle is $F_t = m a_t = mkr$.The power $P$ delivered to the particle is the product of the tangential force and the velocity: $P = F_t \cdot v = (mkr) \cdot (krt) = mk^2r^2t$.

Class 11 Chemistry Data Entry - Chemistry Level 0 of all question bank

$A$ 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 $a_c = k^2rt^2$. The power delivered to the particle by the forces acting on it is

IIT 1994 All IIT

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

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Which of the following is $NOT$ included in in-situ conservation?

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$A$ plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches $30^o$,the box starts to slip and slides $4.0\, m$ down the plank in $4.0\, s$. The coefficients of static and kinetic friction between the box and the plank will be,respectively:

AIPMT 2015

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The basic functional unit of the human kidney is

AIPMT 1997

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Match the following columns:

Column-$I$ Column-$II$

$(A)$ Linnaeus $(i)$ First to discover viruses

$(B)$ Ivanowsky $(ii)$ First to discover lichens

$(C)$ Iyengar $(iii)$ Father of Indian Bryology

$(D)$ Tulasne $(iv)$ Father of Taxonomy

$(E)$ Shiv Ram Kashyap $(v)$ Father of modern Phycology in India

Column-$I$	Column-$II$
$(A)$ Linnaeus	$(i)$ First to discover viruses
$(B)$ Ivanowsky	$(ii)$ First to discover lichens
$(C)$ Iyengar	$(iii)$ Father of Indian Bryology
$(D)$ Tulasne	$(iv)$ Father of Taxonomy
$(E)$ Shiv Ram Kashyap	$(v)$ Father of modern Phycology in India