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: 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 true
- D.Both Statement I and Statement II are false
Show answer and solution
Correct option: B
Solution
Statement I is correct: when tension equals weight (net force = 0), the elevator moves at constant velocity (uniform speed), either up or down — Newton's first law.
Statement II is false: when the elevator goes down with increasing speed, the acceleration is downward, so the net force on the person is downward. This means mg − N = ma, giving N = m(g − a) < mg. The normal force (floor reaction) is LESS than the person's weight, not more.
Statement II is false: when the elevator goes down with increasing speed, the acceleration is downward, so the net force on the person is downward. This means mg − N = ma, giving N = m(g − a) < mg. The normal force (floor reaction) is LESS than the person's weight, not more.
[JEE Main 2023 · 24 Jan · Shift 1 · Paper-1(B.E./B. Tech.)]