Question

When a bicycle is in motion the force of friction exerted by the ground on the two wheels (front and rear) is $ {F_1} $ and $ {F_2} $ respectively. Then:
(A) Both $ {F_1} $ and $ {F_2} $ are in backward direction
(B) $ {F_1} $ is in backward direction and $ {F_2} $ is in forward direction
(C) $ {F_1} $ is in forward direction and $ {F_2} $ is in backward direction
(D) Both $ {F_1} $ and $ {F_2} $ are in forward direction

Answer 1

Hint: To determine the direction of the frictional force acting on each wheel of the bicycle, we first have to imagine a frictionless surface and then observe the direction of the relative motion of both the wheels on the ground. As friction always opposes the relative motion, so its direction on both the wheels will be determined easily.

Complete step by step answer
We know that the force of friction always opposes the relative motion between two surfaces in contact. So for determining the direction of the friction, we first have to determine the direction of relative motion. So we imagine that we are pedaling a cycle on a smooth frictionless ground.

We move a bicycle by rotating its pedals, which are connected to the rear wheel through the chain. So the rear wheel is rotated by our pedaling. This makes the rear wheel rotate. If there is no friction present on the ground, then the wheel will keep on rotating and will not translate forward. The point of the wheel, which is in contact with the ground, moves in the backward direction relative to the ground. So to oppose this motion, the force of friction acts on the wheel in the forward direction and makes it translate forward.
Therefore the direction of $ {F_2} $ is in forward direction.

Now, this forward frictional force is transmitted through the frame of the bicycle to the front wheel of the bicycle, which makes it translate forward. If there is no frictional force between the wheel and the ground, then the front wheel will keep on translating forward and will not rotate. So the point of the wheel in contact with the ground moves in the forward direction relative to the ground. To oppose this relative motion, the frictional force acts in the backward direction and makes it rotate.
Therefore the direction of $ {F_1} $ is in a backward direction.
Thus, $ {F_1} $ is in backward direction and $ {F_2} $ is in forward direction.

Hence, the correct answer is option B.

Note
It is a common misconception that the force of friction always acts opposite to the direction of motion of the moving object. It is true only for pure translational motion. But when there is rotation involved, then we need to use the basic definition of the friction, that it opposes the relative motion of the two surfaces.