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

Hint:We know that when there are even numbers of wheels in a gear system, the direction of driver and driven wheel is opposite. Whereas, in case of an odd number of wheels in the gear system, the driven wheel rotates in the same direction of the driving wheel. Here, we will consider Gear ratio in terms of the number of teeth in the wheels.

Complete step by step answer:
We are given that in a gear system, the gear ratio of the driving wheel A and driven wheel B is $10:1$. Let the number of teeth in wheel A and wheel B be ${N_A}$ and ${N_B}$. Therefore, the gear ratio can be given as,
$\dfrac{{{N_A}}}{{{N_B}}} = \dfrac{{10}}{1}$
Now, to rotate the driven wheel B in the direction of driving wheel A is engaged with another wheel C.Let the number of teeth in the wheel C be ${N_C}$ .This wheel C is engaged between the wheels A and B.Therefore, the ratio of wheel A and C can be given as,
$\dfrac{{{N_A}}}{{{N_C}}} = \dfrac{{10}}{x}$
Similarly, the ratio of wheel C and B can be given as
\[\dfrac{{{N_C}}}{{{N_B}}} = \dfrac{x}{1}\]
\[ \Rightarrow {N_B} = \dfrac{{{N_C}}}{x}\]
Now, we will put this value of ${N_B}$in $\dfrac{{{N_A}}}{{{N_B}}} = \dfrac{{10}}{1}$
$\dfrac{{{N_A} \times x}}{{{N_C}}} = \dfrac{{10}}{1}$
We know that $\dfrac{{{N_A}}}{{{N_C}}} = \dfrac{{10}}{x}$
Therefore, the gear ratio of wheels A and C should be $\dfrac{{{N_A}}}{{{N_C}}} = \dfrac{1}{1}$
Thus, the gear ratio of the wheels A and C is $1:1$.

Hence, option B is the right answer.

Note:Here, we have seen that the ratio of the wheels A and C is $1:1$. This means that the number of teeth on both the wheels A and C are the same. Here, wheel A is engaged with other wheel C to rotate the driven wheel B in the direction of driving wheel A. Wheel C is called the idler gear which does not affect the gear ratio of two main wheels.