Question

which of the following lever arms will produce the greatest torque?
a
b
c
d

Explanation:

Step1: Calculate torque for option A

Torque formula: $\tau = F\times d$. Assume $g = 10m/s^{2}$. For option A, $F_{1}=2mg$, $d_{1}=(30 - 10)cm = 20cm$, $F_{2}=mg$, $d_{2}=(40 - 30)cm = 10cm$. Net torque $\tau_{A}=2mg\times20 - mg\times10=30mg$ (counter - clockwise torque minus clockwise torque).

Step2: Calculate torque for option B

For option B, $F_{1}=2mg$, $d_{1}=(40 - 30)cm = 10cm$, $F_{2}=mg$, $d_{2}=(50 - 30)cm = 20cm$. Net torque $\tau_{B}=mg\times20 - 2mg\times10 = 0$.

Step3: Calculate torque for option C

For option C, $F_{1}=2mg$, $d_{1}=(30 - 0)cm = 30cm$, $F_{2}=mg$, $d_{2}=(60 - 30)cm = 30cm$. Net torque $\tau_{C}=mg\times30 - 2mg\times30=- 30mg$ (clockwise torque greater).

Step4: Calculate torque for option D

For option D, $F_{1}=2mg$, $d_{1}=(30 - 10)cm = 20cm$, $F_{2}=mg$, $d_{2}=(60 - 30)cm = 30cm$. Net torque $\tau_{D}=2mg\times20 - mg\times30=10mg$.

Answer:

A. Option A