Question

In a gear system, the gear ratio of the driving wheel $A$ and driven wheel $B$ is $10:1$. To rotate the driven wheel $B$ in the direction of driving wheel $A$, the driving wheel $A$ is engaged with other wheel $C$. What should be the gear ratio of the wheels $A$ and $C$?

• A. $10:1$
• B. $1:1$
• C. $2:1$
• D. $1:10$

Answer 1

The correct option is B $1:1$

CONCEPT

1)Both driver and driven pulley will rotate in same direction if there is an odd number if ideal gear is assembled between them.

2)1)Both driver and driven pulley will rotate in different direction if there is an even number if ideal gear is assembled between them.

now,gear ratio is given as

$\frac{N_a}{N_b}$=$\frac{10}{1}$

now to obtained same direction of both driver and driven gear we have to mesh an odd number of ideal (intermediate gear) in between them,let's "C"

hence

$\frac{N_a}{N_c}$=$\frac{10}{x}$

also $\frac{N_c}{N_b}$=$\frac{x}{1}$;$N_b$=$\frac{N_c}{x}$

on putting the value of $N_b$ in equation 1 relation we find

$\frac{N_a\times x}{N_c}$=$\frac{10}{1}$

and we know that $\frac{N_a}{N_c}$=$\frac{10}{x}$

so finally we get the gear ratio of $\frac{N_a}{N_c}$=1:1