Question

A gear train shown in the figure consists of gears P, Q, R, and S. Gear Q and gear R are mounted on the same shaft. All the gears are mounted on parallel shafts and the number of teeth of P, Q, R and S are 24, 25, 30 and 80 respectively. Gear P is rotating at 400 rpm. The speed (in rpm). The speed(in rpm) of the gear S is

Answer 1

$T_P=24$
$T_Q=45$ $N_P=400$ rpm
$T_R=30$ $N_s=?$
$T_S=80$
Here gear R is not meshing at all
$\frac{N_P}{N_Q}=\frac{T_Q}{T_P}=\frac{45}{24}$ ... (1)
$\frac{N_Q}{N_S}=\frac{T_S}{T_Q}=\frac{80}{45}$ ... (2)

By $\left(1\right)\times \left(2\right)$
$\frac{N_P}{N_S}=\frac{45}{24}\times \frac{80}{45}$

$N_S=N_p\times \frac{24}{80}=\frac{400\times 24}{80}$
$N_S=120$ rpm