Answer

Verified

386.7k+ views

**Hint:**Use the formula for gear ratio in terms of radius of the driving wheel and radius of the driven wheel and determine the gear ratio for the system of given driving and driven wheels. Also use the formula for gear ratio in terms of the number of teeth in the driving wheel and number of teeth in the driving wheel. Substitute the value of gear ratio and number of teeth in the driven wheel and calculate the required answer.

**Formulae used:**

The gear ratio of the wheels is given by formula

\[{\text{Gear ratio}} = \dfrac{{{\text{Radius of driving wheel}}}}{{{\text{Radius of driven wheel}}}}\] …… (1)

The gear ratio of the wheels is also given by formula

\[{\text{Gear ratio}} = \dfrac{{{\text{Number of teeth driving wheel}}}}{{{\text{Number of teeth driven wheel}}}}\] …… (2)

**Complete step by step answer:**

We have given that the radius \[{r_A}\] of the driving wheel is \[2\,{\text{cm}}\] and the radius \[{r_B}\] of the driven wheel is \[20\,{\text{cm}}\].

\[{r_A} = 2\,{\text{cm}}\]

\[ \Rightarrow{r_B} = 20\,{\text{cm}}\]

Let us calculate first the gear ratio.We can determine the gear ratio using equation (1).Substitute \[{r_A}\] for radius of the driving wheel and \[{r_B}\] for radius of the driven wheel in equation (1).

\[{\text{Gear ratio}} = \dfrac{{{r_A}}}{{{r_B}}}\]

Substitute \[2\,{\text{cm}}\] for \[{r_A}\] and \[20\,{\text{cm}}\] for \[{r_B}\] in the above equation.

\[{\text{Gear ratio}} = \dfrac{{2\,{\text{cm}}}}{{20\,{\text{cm}}}}\]

\[ \Rightarrow {\text{Gear ratio}} = \dfrac{1}{{10}}\]

Hence, the gear ratio for the given system of the driving wheel and driven wheel is \[\dfrac{1}{{10}}\].We have given that the number of teeth in the driven wheel is 40.

\[{n_B} = 40\].We have asked to determine the number of teeth \[{n_A}\] in the driving wheel.Substitute \[{n_A}\] for the number of teeth in the driving wheel and \[{n_B}\] for the number of teeth in the driven wheel in equation (2).

\[{\text{Gear ratio}} = \dfrac{{{n_A}}}{{{n_B}}}\]

Rearrange the above equation for \[{n_A}\].

\[{n_A} = {n_B}\left( {{\text{Gear ratio}}} \right)\]

Substitute 40 for \[{n_B}\] and \[\dfrac{1}{{10}}\] for \[{\text{Gear ratio}}\] in the above equation.

\[{n_A} = 40\left( {\dfrac{1}{{10}}} \right)\]

\[ \therefore {n_A} = 4\]

Therefore, the number of teeth in the driving wheel are 4.

**Hence, the correct option is A.**

**Note:**The students should keep in mind that if the wheels are not specified as the driving wheel and the driven wheel then one should keep in mind that the wheel with more teeth or larger radius is the driven wheel and the wheel with the less teeth or smaller radius is the driving wheel. This will make the process of identifying the wheels easy.

Recently Updated Pages

Cryolite and fluorspar are mixed with Al2O3 during class 11 chemistry CBSE

Select the smallest atom A F B Cl C Br D I class 11 chemistry CBSE

The best reagent to convert pent 3 en 2 ol and pent class 11 chemistry CBSE

Reverse process of sublimation is aFusion bCondensation class 11 chemistry CBSE

The best and latest technique for isolation purification class 11 chemistry CBSE

Hydrochloric acid is a Strong acid b Weak acid c Strong class 11 chemistry CBSE

Trending doubts

Give 10 examples for herbs , shrubs , climbers , creepers

Difference Between Plant Cell and Animal Cell

Write a letter to the principal requesting him to grant class 10 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Name 10 Living and Non living things class 9 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

List some examples of Rabi and Kharif crops class 8 biology CBSE

Write the 6 fundamental rights of India and explain in detail