JEE Main 2023 · 24 January · morning · Single correct · +4 / −1
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) Both Statement I and Statement II are false
- (b) Both Statement I and Statement II are true
- (c) Statement I is false but Statement II is true
- (d) Statement I is true but Statement II is false
Answer and solution
Answer (d) Statement I is true but Statement II is false
Solution
Physics sir · 4 steps
Turn speed into acceleration first: steady speed means a = 0, speeding up downward means a points down.
- Statement I. Uniform speed means zero acceleration, so the net force on the elevator is zero. That happens exactly when the cable tension T equals the weight Mg, whether the elevator moves up or down. True.
- Set up Statement II. Take downward as positive. Two forces act on the person: the weight mg downward and the normal force N from the floor upward. Going down with increasing speed means the acceleration a points downward.
mg - N = ma ⇒ N = m(g - a)
- Statement II. Since a > 0 downward, N = m(g - a) is less than mg. The person feels lighter, not heavier. False.
- So. Statement I is true and Statement II is false, which is option (d).
The idea to keep. In a lift, only the direction of acceleration matters. Acceleration upward makes you feel heavier, N = m(g + a); acceleration downward makes you feel lighter, N = m(g - a).
Answer from the NTA final answer key. Solution by PrepWiser.