Ratios and proportional reasoning Transitional Reasoning Practice

Questions

1. 1.

   A student team investigates how changing physical parameters affects the oscillation period of a simple pendulum. Pendulum B is constructed with a string that is 9 times as long as that of Pendulum A, and its bob has 4 times the mass of Pendulum A's bob. Based on the period relationship $T = 2\pi\sqrt{\frac{L}{g}}$, what is the ratio of the period of Pendulum B to that of Pendulum A, $T_B / T_A$?

   • A) 36
   • B) 6
   • C) 4
   • D) 3
2. 2.

   An engineering team tests two prototype rovers navigating separate circular tracks on a test course. Rover B travels at three times the speed of Rover A, while navigating a circular path with a radius six times that of Rover A. Based on the relationship for centripetal acceleration, $a_c = \frac{v^2}{r}$, what is the ratio of the centripetal acceleration of Rover B to that of Rover A, $\frac{a_B}{a_A}$?

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

   A laboratory technician prepares two solid cylindrical copper ingots, designated as Ingot X and Ingot Y, to calibrate a high-precision scale. Ingot Y has twice the diameter and one-third the height of Ingot X. Assuming both ingots have a uniform density throughout, what is the ratio of the mass of Ingot Y to the mass of Ingot X, $m_Y / m_X$?

   • A) $2/3$
   • B) $3/4$
   • C) $4/3$
   • D) $8/3$

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