Question

Statement-1: A cyclist always bends inwards while negotiating a curve.

Statement-2: By bending he lowers his centre of gravity

A. Statement-1 is true, statement-2 is true, statement-2 is correct explanation for statement-1

B. Statement-1 is true, statement-2 is true, statement-2 is NOT the correct explanation for statement-1

C. Statement-1 is true, statement-2 is false

D. Statement-1 is false, statement-2 is true

Answer 1

Hint: Forces acting on the cycle in different axes are centripetal force and frictional force.

Complete step-by-step answer:

From the figure additional force to bend at the centre

Therefore, from the deviation angle $\theta $ we can give

$f + R\sin \theta = \dfrac{{m{v^2}}}{R}$

Where $\dfrac{{m{v^2}}}{R}$ is the centripetal force.

Centripetal Force: A force that makes a body follows a curved path. Its direction is always orthogonal to the motion of the body and towards the fixed point of the instantaneous center of curvature of the path.

Center of gravity: A point from which the weight of a body or system may be considered to act. In uniform gravity it is the same as the centre of mass.

The weight W, acts vertically downward and the normal force, N acts vertically upward. The frictional force, F, of the road acts horizontally in the direction of which the cyclist is turning. The frictional force provides the centripetal force necessary to turn the cyclist. But the frictional force also produces a torque that will cause the rider and bicycle to tip outwards. When the cyclist lean inward the normal force of the road does not act through the center of gravity thus producing an opposite torque that cancels out the torque provided by the frictional force. Thus there is no tendency for the cyclist to tip outwards.

Statement-1 is true and Statement-2 is true, statement-1 is not the correct explanation for statement-1.

Therefore, Option B is the correct answer.

Note: An object needs the centripetal force to keep in a circular motion. The direction of force is towards the center of the circle of motion, and its magnitude and direction can both be derived from a consideration of Newton's second law of motion. This force is usually gravity.