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:
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:
- Statement I is false but Statement II is true
- Statement I is true but Statement II is false
- Both statement I and Statement II are false
- Both Statement I and Statement II are true
The Correct Option is B
Solution and Explanation
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
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Concepts Used:
Newtons Laws of Motion
Newton’s First Law of Motion:
Newton’s 1st law states that a body at rest or uniform motion will continue to be at rest or uniform motion until and unless a net external force acts on it.
Newton’s Second Law of Motion:
Newton’s 2nd law states that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the object’s mass.
Mathematically, we express the second law of motion as follows:
Newton’s Third Law of Motion:
Newton’s 3rd law states that there is an equal and opposite reaction for every action.