Question

The gearing of a machine tool is shown in the below figure. The motor shaft is connected to gear A and rotates at 975 rpm. The gear wheels B, C, D, and E are fixed to parallel shafts rotating together. The final gear F is fixed on the output shaft. What is the speed of gear F? The number of teeth on each gear are as follows: \( A=20 \), \( B=50 \), \( C=25 \), \( D=75 \), \( E=26 \), and \( F=65 \). 

• A. 78 rpm
• B. 104 rpm
• C. 52 rpm
• D. 98 rpm

Hint:

- Gear speed formula: \( N_F = N_A \times \frac{T_A}{T_B} \times \frac{T_C}{T_D} \times \frac{T_E}{T_F} \). - Speed decreases with increasing teeth ratio. - Always multiply through each stage for final speed.

Answer 1

The Correct Option is C

Step 1: Formula for gear speed. \[ N_F = N_A \times \left(\frac{T_A}{T_B}\right) \times \left(\frac{T_C}{T_D}\right) \times \left(\frac{T_E}{T_F}\right) \]
Step 2: Substituting values. \[ N_F = 975 \times \left(\frac{20}{50}\right) \times \left(\frac{25}{75}\right) \times \left(\frac{26}{65}\right) \] \[ N_F = 975 \times 0.4 \times 0.3333 \times 0.4 \] \[ N_F = 52 \text{ rpm} \] Thus, the correct answer is (c) 52 rpm.