Question

0.2 kg ball rotates at a constant of 3m/s on the end of 1.2 m long string. The string describes a horizontal circle. What is the centripetal acceleration of the object ? ​

Answer 1

$\large\bold{\underline{\underline{{Given:-}}}}$

${\bullet\:}$ Mass of the ball  = 0.2 kg

${\bullet\:}$ Length of the string = 1.2 cm

${\bullet\:}$ Velocity = 3 m/s

$\large\bold{\underline{\underline{{To\:Find:-}}}}$

${\bullet\:}$ The centripetal acceleration of the object.

$\large\bold{\underline{\underline{{Solution:-}}}}$

$\large\boxed{\underline{\pink{\sf a =\dfrac{v^{2} }{r}  }}}$

Here,

➣ a = centripetal acceleration

➣ v = velocity

➣ r = radius

Units :-

➣ a = metres per second (m/s)

➣ v = metres per second (m/s)

➣ r = metre (m)

According to the question :-

➣ a = ?

➣ v = 3 m/s

➣ r = 1.2 m

${\bullet\:}$ We should find the centripetal acceleration of the body.

${\bullet\:}$ Substituting the values...we get,

$\purple{\implies\:}$ $\sf{a=\dfrac{(3\:ms^{-1} )^{2} }{1.2\:m} }$

$\purple{\implies\:}$ $\sf{a=\dfrac{9\:m^{2}\:s^{-2}  }{1.2\:m} }$

$\purple{\implies\:}$ $\sf{a=\dfrac{9\:ms^{-2}  }{1.2\:m} }$

$\purple{\implies\:}$ $\sf{a=7.5\:ms^{-2} }$

$\large\boxed{\underline{\pink{\sf \therefore Centripetal \:acceleration \:  of\:the\:ball=7.5\:m/s}}}$

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Answer 2

Given info : 0.2 kg ball rotates at a constant of 3m/s on the end of 1.2 m long string. The string describes a horizontal circle.

To find : the centripetal acceleration of the object is ..

solution : length of the string , l = 1.2 m

speed of the ball attached to one of the ends of string, v = 3 m/s

mass of ball , m = 0.2 kg

for a uniform circular motion, the centripetal acceleration of the object is given by, a =  $\frac{v^2}{r}$

a = $\frac{3^2}{1.2}=7.5m/s^2$

therefore the centripetal acceleration of the object is 7.5 m/s².

[ note : centripetal acceleration is directed radially towards the centre of the circular path. so the centripetal force also acts towards the centre of it and to balance this force, a psuedo force needs to apply just opposite to this force, known as centrifugal force. ]