JEE Advanced 2017 Paper 2

Distance of F1 from the point Q increases
⇒ Torque F1 increases (clockwise)
Distance of force Mg from Q decreases.
⇒torque of Mg decreases (anti clockwise)
⇒ Net torque is anti-clockwise direction increases
⇒ τ ≠ 0  Incorrect
(B) Net torque = 0  correct
(C) As the wheel begins to climb, the distance of the force F3 from point Q increases initially
⇒ Torque of F3 through X increases clockwise
Torque of mg decreases anticlockwise
⇒ Net torque increases clockwise initially  Incorrect
(D) When force is applied vertically, then there will be no normal reaction atpoint Q and hence friction will also be zero.
This will cause slipping of the wheel. Since, it is given that there is no slipping at point Q, therefore we can write
τ=F4(2Rcosθ)−MgRcosθ(Clock wise)
τ=(2F4R−MgR)cosθ
As θ increases from 0 to

π

2

,cosθ decreases fro 1 to 0
⇒τ decreases as the wheel climbs.  Correct