Question

A ladder is more apt when you are high up on its rung than when you are just beginning to climb. Why?
A. When you are high up, the moment of force tending to rotate the ladder about its base increases, while in the latter case, the moment of force is insufficient to cause slipping.
B. When you are high up, the ladder is in unstable equilibrium.
C. As you climb up, your potential energy increases.
D. When you are high up, the centre of gravity of the system shifts upwards so the ladder is unstable, while in the latter case the system is more stable.

Answer 1

Hint:Check all the options given in the question carefully. Check when a person climbs up on the ladder, the forces acting on the system of the person and ladder are balanced or not. Also check whether the increase in potential energy of the person makes the ladder unstable. Also check the effect of change in position of centre of gravity of the ladder or moment of force of the ladder due to the weight of the person on the ladder.

Formula used:
The moment of force or torque \[\tau \] acting on an object is given by
\[\tau = rF\] …… (1)
Here, \[F\] is the force acting on the object and \[r\] is the perpendicular force between the point of action of the force and the centre of the torque.

Complete answer:
When one climbs up the ladder, the weight of the person is balanced by the normal force of ladder on the person and weight of the ladder is balanced by the normal force of ground on the ladder. The frictional force is also balanced by the components of the reaction forces.Hence, when one climbs up on the ladder, all the vertical and horizontal forces cancel each other. Therefore, the ladder is in equilibrium.Hence, the option A is incorrect.

When one climbs up on the ladder, the potential energy of the person definitely increases. But according to the law of conservation of energy, the total energy involved in this system gets balanced and the ladder remains in equilibrium.Hence, the option C is incorrect.

When a person climbs up on the ladder, the centre of gravity of the ladder and the person system shifts due to the additional weight of the person and this centre of gravity shifts up. But this shifting of centre of gravity is to balance the system.Therefore, the system does not become unstable when the centre of gravity of the system shifts up.Hence, the option D is incorrect.

From equation (1), we can conclude that the moment of force depends on the perpendicular distance between the force and centre of the torque.When the person moves up, the distance between the person’s weight and the base of the ladder which is the centre of the torque increases. Hence, the torque or moment of force of the ladder about the base also increases which causes the ladder to be unstable.The moment of inertia due to weight of the person at the base of the ladder is very small or may be zero. Hence, the ladder remains stable.

Hence, the correct option is A.

Note: The students should keep in mind that we have considered the moment of force or torque on the ladder only at its base because the torque about the base of the ladder due to the extra weight of the person on the ladder can only cause the ladder to change the equilibrium of the ladder as the ladder is in equilibrium before the person climbs on it.