Question

If the tension in the cable supporting an elevator is equal to the weight of the elevator, the elevator may be
(This question has multiple correct options)
A). Going up with increasing speed
B). Going down with increasing speed
C). Going up with uniform speed
D). Going down with uniform speed

Answer 1

Hint: When a body is accelerating then its velocity is changing and there is additional force in the system but if acceleration of the body is zero then the body stays at rest or in a state of uniform motion.

Complete step by step answer:
According to Newton’s second law of motion, when a force acts on a body then an acceleration is produced which changes the state of the body. The opposite of this statement is also true that when an acceleration acts on a body, a force comes into picture changing the velocity of the body.
Tension is the force in a string produced due to the weight of a body. Greater the weight of a body, greater the gravity acting on it and greater is the tension in the string by which that body is hanging. In the case of an elevator, the direction of tension is vertically upwards and is directly proportional to the magnitude of gravitational force of attraction acting on the body.
Now, if there is some acceleration in the elevator motion then there is some additional force acting on the system due to gravity. If this additional force acts in upward direction then the tension in the cable decreases while if the force acts in downward direction, the tension increases. This implies that the elevator is not in uniform motion.

We are given that tension in the elevator is equal to the weight of the elevator which implies that there is no acceleration taking place and the elevator is in a state of uniform motion which can be either in upward or downward direction.
Hence, both option B and C are correct.

Note: If there is acceleration in a system then it corresponds to a force according to Newton’s second law. If there is acceleration in a body then it means that velocity is changing and the body is no longer in the state of rest or uniform motion.