A gear train is as shown in the figure below, in which gears A and B have 20 and 40 teeth, respectively. If arm C is fixed and gear A rotates at 100 r.p.m., the speed of gear B will be

F1 M.J Madhu 03.04.20 D1

This question was previously asked in
ESE Mechanical 2018 Official Paper
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  1. 90 r.p.m.
  2. 75 r.p.m.
  3. 50 r.p.m.
  4. 20 r.p.m.

Answer (Detailed Solution Below)

Option 3 : 50 r.p.m.
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Detailed Solution

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Concept:

Speed ratio between two mating gears is given by \(\frac{{{N_A}}}{{{N_B}}} = \frac{{{T_B}}}{{{T_A}}}\)

Calculation:

Motions

Arm

Rotation of Gear A

Rotation of Gear B

The arm is fixed and Gear A rotates by x rpm

0

x

\(- \frac{{{T_A}}}{{{T_B}}}x\)

Arm Free

y

y + x

\(y - \frac{{{T_A}}}{{{T_B}}}x\)

                      

Given that Arm is fixed ∴ y = 0 and NA = 100 r.p.m.

Then \({N_B} = - \;\frac{{20}}{{40}} \times 100 = - \;50\;r.p.m.\)

Note: Sign is important when the options are given with the same magnitude but with different directions. In this question, the negative sign of B means that if gear A was rotating in the clockwise direction then gear B will rotate in the anticlockwise direction.

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