Question

A vehicle of mass \( 200 \, \text{kg} \) is moving along a levelled curved road of radius \( 70 \, \text{m} \) with angular velocity of \( 0.2 \, \text{rad/s} \). The centripetal force acting on the vehicle is:

Answer 1

The centripetal force (F) required to keep an object of mass m moving in a circular path of radius r with angular velocity ω is given by:
\(F = mω^2r\)
In this case, the mass of the car is 200 kg, the radius of the circular track is 70 m, and the angular velocity of the car is 0.2 rad/s. 
Substituting these values into the above formula, we get:
F = \((200 kg) * (0.2 rad/s)^2 * (70 m) = 560 N\)
Therefore, the centripetal force required to keep the car moving in a circular track of radius 70 m with angular velocity of 0.2 rad/sec is 560 N.
So, Answer is 560.

Answer 2

The centripetal force is given by the formula: \[ F_c = m \omega^2 r, \] where \( m = 200 \, \text{kg} \) is the mass of the vehicle, \( \omega = 0.2 \, \text{rad/s} \) is the angular velocity, and \( r = 70 \, \text{m} \) is the radius of the curved road. Substitute the values: \[ F_c = 200 \times (0.2)^2 \times 70. \] Simplify: \[ F_c = 200 \times 0.04 \times 70 = 560 \, \text{N}. \] Thus, the centripetal force acting on the vehicle is \( \boxed{560 \, \text{N}} \).