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Discussion Forum



1)

A wheel of radius R and mass M is placed at the bottom of a fixed step of height R as shown in the figure. A constant force is continuously applied on the surface of the wheel so that it just climbs the step without slipping. Consider the torque  $\tau$ about an axis normal to the plane of the paper passing through the point Q. Which of the following options is/are correct ?

812020948_too.JPG


A) If the force is applied normal to the circumference at point P then $\tau$ is zero

B) if the force is applied tangentially at point S then $\tau\neq 0$ but the wheel never climbs the step

C) If the force is applied at point P tangentially , then $\tau$ decreases continously as the wheel climbs

D) If the force is applied normal to the circumfernce at point X , then $\tau $ is constant

Answer:

Option A,C

Explanation:

812020225_ww.JPG

(a) If force is applied normal to surface at  P, then the line of action of force will pass from  Q and thus $\tau$ =0

(b) wheel can climb

(c) $\tau=F(2R\cos\theta)-mgR\cos\theta$

             $\tau\propto\cos\theta$

812020554_re.JPG

Hence, as θ increases, $\tau$ decreases so it correct

(d)

     81202089_str.JPG

$  \tau =Fr_{\perp}-mg\cos\theta:\tau$ increases with θ