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 

In the light of the above statements, choose the correct answer from the options given below:

• A. Statement I is false but Statement II is true
• B. Statement I is true but Statement II is false
• C. Both statement I and Statement II are false
• D. Both Statement I and Statement II are true

Answer 1

The Correct Option is B

Statement-1:

When the elevator is moving with uniform speed, the tension in the rope is equal to the gravitational force:

\[ T = F_g \]

Where \( T \) is the tension in the rope, and \( F_g \) is the gravitational force acting downward.

Statement-2:

When the elevator is going down with increasing speed, its acceleration is downward. The force balance equation can be written as:

\[ W - N = \frac{W}{g} \times a \]

Simplifying the equation:

\[ N = W \left(1 - \frac{a}{g}\right) \]

Hence, the normal force \( N \) is less than the weight \( W \), since the elevator's downward acceleration reduces the normal force felt by the object inside the elevator.

Therefore, Statement I is true but Statement II is false