(A) Length of the string,$r = 80\; cm = 0.8\; m$.Number of revolutions $= 14$,Time taken $= 25\; s$.Frequency,$\nu = \frac{\text{Number of revolutions

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$9.91\; m/s^2$ directed towards the center

(A) Length of the string,$r = 80\; cm = 0.8\; m$.Number of revolutions $= 14$,Time taken $= 25\; s$.Frequency,$\nu = \frac{\text{Number of revolutions}}{\text{Time taken}} = \frac{14}{25}\; Hz$.Angular frequency,$\omega = 2\pi\nu = 2 \times \frac{22}{7} \times \frac{14}{25} = \frac{88}{25}\; rad/s = 3.52\; rad/s$.Centripetal acceleration,$a_c = \omega^2 r = (3.52)^2 \times 0.8$.$a_c = 12.3904 \times 0.8 = 9.91232\; m/s^2 \approx 9.91\; m/s^2$.The direction of centripetal acceleration is always directed along the radius towards the center of the circular path.

Class 11 Physics 3-2.Motion in Plane Non-uniform Circular Motion (Centrifugal/Centripetal and tangential Accelaration)

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$A$ stone tied to the end of a string $80\; cm$ long is whirled in a horizontal circle with a constant speed. If the stone makes $14$ revolutions in $25\; s$,what is the magnitude and direction of acceleration of the stone?

A
$9.91\; m/s^2$ directed towards the center
B
$8.91\; m/s^2$ directed towards the center
C
$7.91\; m/s^2$ directed towards the center
D
$6.91\; m/s^2$ directed towards the center

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3-2.Motion in Plane

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Non-uniform Circular Motion (Centrifugal/Centripetal and tangential Accelaration)

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$A$ stone tied to the end of a string $80\; cm$ long is whirled in a horizontal circle with a constant speed. If the stone makes $14$ revolutions in $25\; s$,what is the magnitude and direction of acceleration of the stone?

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