Ratios and proportional reasoning Knowledge-Based Practice

Questions

1. 1.

   The electrical resistance of a uniform wire of length $L$ and cross-sectional area $A$ is given by $R = \rho \frac{L}{A}$, where $\rho$ is resistivity. If the length of the wire is doubled while its cross-sectional area is quadrupled, by what factor does its resistance change?

   • A) $\frac{1}{2}$
   • B) 2
   • C) $\frac{1}{8}$
   • D) 8
2. 2.

   The centripetal acceleration of an object moving in a circle of radius $r$ at speed $v$ is given by $a = \frac{v^2}{r}$. If the radius of the circular path is doubled while the speed of the object is halved, by what factor does the centripetal acceleration change?

   • A) $\frac{1}{8}$
   • B) $\frac{1}{4}$
   • C) $\frac{1}{2}$
   • D) 1
3. 3.

   The kinetic energy of an object of mass $m$ moving at speed $v$ is given by $K = \frac{1}{2}mv^2$. If the mass of the object is halved while its speed is tripled, by what factor does its kinetic energy change?

   • A) It increases by a factor of 4.5.
   • B) It increases by a factor of 1.5.
   • C) It increases by a factor of 3.0.
   • D) It increases by a factor of 9.0.

Answers and step-by-step solutions appear after you finish the test.