Answer:
The tension in the string is quadrupled i.e. increased by a factor of 4.
Explanation:
The tension in the string is the centripetal force. This force is given by
[tex]F = \dfrac{mv^2}{r}[/tex]
m is the mass, v is the velocity and r is the radius.
It follows that [tex]F \propto v^2[/tex], provided m and r are constant.
When v is doubled, the new force, [tex]F_1[/tex], is
[tex]F_1 = \dfrac{m(2v)^2}{r} = \dfrac{4mv^2}{r} = 4\dfrac{mv^2}{r} = 4F[/tex]
Hence, the tension in the string is quadrupled.
When the angular speed of the mass is doubled the tension on the string will be quadrupled.
The tension on string for the horizontal circle is calculated as follows;
[tex]T = \frac{mv^2}{r}= m\omega^2 r[/tex]
where;
[tex]\\\\\frac{T_1}{\omega_1^2} = \frac{T_2}{\omega _2^2} \\\\T_2 = \frac{T_1\omega _2^2}{\omega _1^2} \\\\T_2 = \frac{T_1 \times (2\omega_1)^2}{\omega _1^2} \\\\T_2= 4T_1[/tex]
Thus, when the angular speed of the mass is doubled the tension on the string will be quadrupled.
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