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Two mating spur gears have 40 and 120 teeth respectively. The pinion rotates at 1200 rpm and transmits a torque of 20 Nm. The torque transmitted by the gear is      
  • a)
    6.6 Nm  
  • b)
    20 Nm  
  • c)
    40 Nm    
  • d)
    60Nm  
Correct answer is option 'D'. Can you explain this answer?
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Two mating spur gears have 40 and 120 teeth respectively. The pinion r...
 
 
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Two mating spur gears have 40 and 120 teeth respectively. The pinion r...
Given:
- Pinion teeth (N1) = 40
- Gear teeth (N2) = 120
- Pinion speed (N1) = 1200 rpm
- Pinion torque (T1) = 20 Nm

To find:
- Gear torque (T2)

Formula used:
- Torque ratio = (Teeth ratio) * (Speed ratio)

Solution:
1. Teeth ratio:
The teeth ratio is given by the formula:

Teeth ratio = (Number of teeth on gear) / (Number of teeth on pinion)

Substituting the given values:

Teeth ratio = N2 / N1 = 120 / 40 = 3

2. Speed ratio:
The speed ratio is given by the formula:

Speed ratio = (Speed of pinion) / (Speed of gear)

Substituting the given values:

Speed ratio = N1 / N2 = 1200 rpm / 1 rpm = 1200

3. Torque ratio:
Using the formula for torque ratio:

Torque ratio = (Teeth ratio) * (Speed ratio) = 3 * 1200 = 3600

4. Finding gear torque:
The torque transmitted by the gear (T2) can be found by rearranging the torque ratio formula:

T2 = (Torque ratio) * T1 = 3600 * 20 Nm = 72000 Nm = 60 Nm

Therefore, the torque transmitted by the gear is 60 Nm, which corresponds to option (d) in the given options.
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Two mating spur gears have 40 and 120 teeth respectively. The pinion r...
D
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Two mating spur gears have 40 and 120 teeth respectively. The pinion rotates at 1200 rpm and transmits a torque of 20 Nm. The torque transmitted by the gear is a)6.6 Nm b)20 Nm c)40 Nm d)60Nm Correct answer is option 'D'. Can you explain this answer?
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