A stone with a mass of 0.70 kg is attached to one end of a string 0.80 m long. The string will break if its tension exceeds 65.0 N. The ston

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A stone with a mass of 0.70 kg is attached to one end of a string 0.80 m long. The string will break if its tension exceeds 65.0 N. The stone is whirled in a horizontal circle on a frictionless tabletop; the other end of the string remains fixed. Find the maximum speed the stone can attain without breaking the string.

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  1. Answer:

    The maximum speed the stone can attain without breaking the string is 8.62 m/s .

    Explanation:

    Given :

    Mass of stone , m = 0.7 kg .

    Length of string , l = 0.8 m .

    It is also given that the stone will break if its tension exceeds 65.0 N.

    Now , we know tension in the rope due to rotation is equal to the centripetal acceleration .

    Therefore , the maximum speed the stone can attain without breaking the string is less than or equal to 65 N .

    So , [tex]\dfrac{mv^2}{r}=65[/tex]

    Putting all value in above equation we get :

    [tex]\dfrac{0.7\times v^2}{0.8}=65\\\\v= 8.62\ m/s[/tex]

    Therefore , maximum speed the stone can attain without breaking the string is 8.62 m/s .

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