Question

Gear 2 rotates at 1200 rpm in a counter clockwise direction and engages with Gear 3 and Gear 4 mounted on the same shaft. Gear 5 engages with Gear 4. The numbers of teeth on Gears 2, 3, 4 and 5 are 20, 40, 15 and 30, respectively. The angular speed of Gear 5 is

• A. 300 rpm counter clockwise
• B. 300 rpm clockwise
• C. 4800 rpm counter clockwise
• D. 4800 rpm clockwise

Answer 1

The correct option is A 300 rpm counter clockwise

Method -I:

Gears	2	3	4	5
Teeth on gears	20	40	15	30
Speed of gears in RPM	-1200	$\frac{+20\times 1200}{40}$	$\frac{+20\times 1200}{40}$	$\frac{-20\times 1200}{40}\times \frac{15}{30}$

$\therefore$ Angular speed of gear 5

$=\frac{-20\times 1200\times 15}{40\times 30}=-300\text{rpm}$

$=300\text{rpm {counter clockwise}}$

Given data:

$N_2=-1200\text{rpm}=1200\text{rpm (ccw)}$

$T_2=20,T_3=40,T_4=15,T_5=30,N_5=?$

Speed ratio:

$\frac{N_5}{N_2}=\frac{T_2\times T_4}{T_5\times T_3}$

$N_5=N_2\left(\frac{T_2\times T_4}{T_5\times T_3}\right)$

$=-1200\left(\frac{20\times 15}{40\times 30}\right)=-300\text{rpm}$

$=300\text{rpm (ccw)}$