Explanation:
The maximum mass that can be hung from a string, m = 10 kg
Length of the string, l = 2 m
Mass of the object, m = 0.5 kg
Let v is the maximum speed that the mass can attain under these conditions without the string breaking. If T is the maximum tension in the string. So,
[tex]T_{max}=mg[/tex]
[tex]T_{max}=10\times 9.8=98\ N[/tex]
The centripetal force is provided by the tension in the string such that :
[tex]T_{max}=\dfrac{mv^2}{r}[/tex]
[tex]v=\sqrt{\dfrac{T_{max}r}{m}}[/tex]
[tex]v=\sqrt{\dfrac{98\times 2}{0.5}}[/tex]
v = 19.79 m/s
or
v = 20 m/s
So, the maximum speed that the mass can attain under these conditions without the string breaking is 20 m/s. Hence, this is the required solution.
