Correct Answer - Option 1 : 1 kN and 0.5 kNm

__Concept:__

Tangential force, T = r × F

Power, P = T × ω

Velocity, V = r × ω

Where P is power (W), r is the radius of the gear (m), ω is angular speed (rad/s), T is torque (Nm), F is tangential force (N), V is Velocity in (m)

**Calculation:**

**Given:**

P = 10 kW = 10000 W, V = 10 m/s, Diameter D = 1 m, ∴ r = 0.5 m

V = r × ω

10 = 0.5 × ω

ω = 20 rad/s

P = T × ω

10000 = T × 20

**T = 500 Nm = 0.5 kNm**

T = r × F

500 = 0.5 × F

**F = 1000 N = 1 kN**