(c) $a = \frac{{{v^2}}}{r} = {\omega ^2}r$ $ = 4{\pi ^2}{n^2}r = 4{\pi ^2}{\left( {\frac{{22}}{{44}}} \right)^2} \times 1$ $ = {\pi ^2}\,m/{s^2}

${\pi ^2}\;m{s^{ - 2}}$ and direction along the radius towards the centre

(c) $a = \frac{{{v^2}}}{r} = {\omega ^2}r$ $ = 4{\pi ^2}{n^2}r = 4{\pi ^2}{\left( {\frac{{22}}{{44}}} \right)^2} \times 1$ $ = {\pi ^2}\,m/{s^2}$ and its direction is always along the radius and towards the centre.

3-2.Motion in PlaneMedium

A stone ties to the end of a string $1\,m$ long is whirled in a horizontal circle with a constant speed. If the stone makes $22$ revolution in $44$ seconds, what is the magnitude and direction of acceleration of the stone

[AIPMT 2005]

A
$\frac{{{\pi ^2}}}{4}\;m{s^{ - 2}}$ and direction along the radius towards the centre
B
${\pi ^2}\;m{s^{ - 2}}$ and direction along the radius away from the centre
C
${\pi ^2}\;m{s^{ - 2}}$ and direction along the radius towards the centre
D
${\pi ^2}\;m{s^{ - 2}}$ and direction along the tangent to the circle

Std 11
Physics

An object of mass $m$ moves with constant speed in a circular path of radius $R$ under the action of a force of constant magnitude $F$. The kinetic energy of object is ............

Medium

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A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius $9 \mathrm{~m}$ and completes $120$ revolutions in $3$ minutes. The magnitude of centripetal acceleration of monkey is (in $\mathrm{m} / \mathrm{s}^2$ ):

Difficult

[JEE MAIN 2024]

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A ball of mass $( m )=0.5 \ kg$ is attached to the end of a string having length $(L)$ $=0.5 m$. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is $324 \ N$. The maximum possible value of angular velocity of ball (in radian/s) is

Difficult

[IIT 2011]

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A particle moves in a circular path of radius $R$ with an angular velocity $\omega = a -bt$ where $a$ and $b$ are positive constants and $t$ is time. The magnitude of the acceleration of the particle after time $\frac {2a}{b}$ is

Medium

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A stone ties to the end of a string $1\,m$ long is whirled in a horizontal circle with a constant speed. If the stone makes $22$ revolution in $44$ seconds, what is the magnitude and direction of acceleration of the stone

Similar Questions

An object of mass $m$ moves with constant speed in a circular path of radius $R$ under the action of a force of constant magnitude $F$. The kinetic energy of object is ............

Certain neutron stars are believed to be rotating at about $1\,rev/\sec $. If such a star has a radius of $ 20\, km$, the acceleration of an object on the equator of the star will be

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A ball of mass $( m )=0.5 \ kg$ is attached to the end of a string having length $(L)$ $=0.5 m$. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is $324 \ N$. The maximum possible value of angular velocity of ball (in radian/s) is

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