There is an obstruction of height h in front of a wheel of radius r weighing W. What is the minimum horizontal force that is to be applied at the centre O of the wheel to overcome the obstruction? Given, h ltr.

There is an obstruction of height h in front of a wheel of radius r we

1.	There is an obstruction of height h in front of a wheel of radius r weighing W. What is the minimum horizontal force that is to be applied at the centre O of the wheel to overcome the obstruction? Given, h ltr.
Answer» Solution :The wheel touches the obstacle at point B FIG. Suppose a force F attempts to turn the wheel about the point B. Weight of wheel W , on the other HAND, resists this ROTATION. Hence to overcome the obstacle MOMENT of the force F about B must be GREATER than the moment of W about B. For F to be minimum, `FxxBD=WxxBC` Here, BD = OC = OA-AC=r-h BC = `sqrt(OB^(2)-OC^(2))=sqrt(r^(2)-(r-h)^(2))=sqrt(2rh-h^(2))` Hence, F (r-h) = W` sqrt(2rh-h^(2))` or, F = `(Wsqrt(2rh-h^(2)))/(r-h)`.