Question

when a rock tied to a string is whirled in a horizontal circle, doubling the speed ________. view available hint(s) doubles the tension in the string doubles the velocity, but the string tension remains the same decreases the velocity quadruples the tension in the string submit

Explanation:

Step1: Recall centripetal - force formula

The centripetal force $F_c$ acting on the rock is provided by the tension $T$ in the string. The centripetal - force formula is $F_c = T=\frac{mv^{2}}{r}$, where $m$ is the mass of the rock, $v$ is the speed of the rock, and $r$ is the radius of the circular path.

Step2: Analyze the effect of doubling the speed

Let the initial speed be $v_1$ and the initial tension be $T_1=\frac{mv_1^{2}}{r}$. When the speed is doubled, $v_2 = 2v_1$. Then the new tension $T_2=\frac{m(2v_1)^{2}}{r}=\frac{m\times4v_1^{2}}{r}=4\times\frac{mv_1^{2}}{r}=4T_1$.

Answer:

D. quadruples the tension in the string