when a rock tied to a string is whirled in a horizontal circle, doubling the speed ________. view available…

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

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

Answer

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