Question

Given below are two statements:

Statement I: An elevator can go up or down with uniform speed when its weight is balanced with the tension of its cable.

Statement II: Force exerted by the floor of an elevator on the foot of a person standing on it is more than his/her weight when the elevator goes down with increasing speed.

Options:
a. Both statements are true, and Statement II is the correct explanation of Statement I.
b. Both statements are true, but Statement II is not the correct explanation of Statement I.
c. Statement I is true, but Statement II is false.
d. Statement I is false, but Statement II is true.

Answer 1

Statement I is true as an elevator can move uniformly up or down when the tension in the cable balances the weight of the elevator. Statement II is false because when an elevator accelerates downward, the normal force is less than the person's weight. Hence, the correct answer is c, Statement I is true and Statement II is false.

Step-by-step explanation:

Regarding Statement I, an elevator can indeed move up or down with uniform speed (constant velocity) when the net force on it is zero, which means the tension in the cable is balanced with the combined weight of the elevator and its contents. This is due to Newton's first law of motion stating that an object in motion will stay in motion with the same speed and direction unless acted upon by an unbalanced force.

As for Statement II, the force exerted by the floor of the elevator on the foot of a person standing in it (normal force) can be greater than the person's weight when the elevator is accelerating upwards, not when it is going down with increasing speed. When the elevator accelerates downward, the normal force experienced by the person decreases. Thus, when the elevator goes down with increasing speed (accelerating downwards), the normal force would be less than the person's weight.

Therefore, the correct answer is option c. Statement I is true, but Statement II is false.