Concepts Of Physics MCQ Edition [Volume 1]PhysicsCircular Motion
A block of mass m is kept on a horizontal ruler. The friction coefficient between the ruler and the block is . One end of the ruler is fixed, and the block is located at a distance L from this fixed end. The ruler is rotated in the horizontal plane about the fixed end. If the angular speed of the ruler is uniformly increased from zero with an angular acceleration , at what angular speed will the block slip?
Options
- A[ ( g L )^2 - ^2 ]^ 1/4
- B[ ( g L )^2 + ^2 ]^ 1/4
- C[ g L - ]^ 1/2
- D[ ( g L )^2 - ^2 ]^ 1/2
Correct answer
A. [ ( g L )^2 - ^2 ]^ 1/4
Step-by-step solution
The block moving in a circular path experiences two components of acceleration: Centripetal acceleration towards the center, a_c = ^2 L Tangential acceleration along the circular path, a_t = L Since these two accelerations are perpendicular to each other, the net acceleration of the block is: a = a_c^2 + a_t^2 = ( ^2 L)^2 + ( L)^2 = L ^4 + ^2 The net force required to keep the block moving with the ruler is provided by the static friction between the block and the ruler. The maximum static friction available is f_