Question

A boy is whirling a stone around his head by means of a string. The string makes one complete revolution every second, and the tension in the string is directed horizontally. The boy then speeds up the stone, keeping the radius of the circle constant, so that the string makes two complete revolutions every second. What happens to the tension in the sting?The tension reduces to one-fourth of its original value.The tension is unchanged.The tension reduces to half of its original value.The tension increases to four times its original value.The tension increases to twice its original value.

Answer 1

Answer:

The tension increases to four times its original value.

Explanation:

v = Velocity

r = Radius

m = Mass of stone

The centripetal force is

$F_c=m\dfrac{v^2}{r}$

The tension will balance the centripetal force

$T=m\dfrac{v^2}{r}$

$\\\Rightarrow T\propto v^2$

$\dfrac{T_1}{T_2}=\dfrac{v_1^2}{v_2^2}\\\Rightarrow \dfrac{T_1}{T_2}=\dfrac{v_1}{2^2v_1^2}\\\Rightarrow \dfrac{T_1}{T_2}=\dfrac{1}{4}\\\Rightarrow T_2=4T_1$

The new tension will be 4 times the old tension