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 true but Statement II is false

Both Statement I and Statement II are false

Both Statement I and Statement II are true

Statement I is false but Statement II is true

Laws of Motion PYQ — JEE Main 2023 · 24 Jan · Shift 1 · Q61 with Solution

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Correct answer: D

For an elevator of mass $m$ , the forces are:

If the elevator moves with uniform speed, then its acceleration is zero: $a=0$

By Newton’s second law, $T - mg = 0$ $T = mg$

So when the tension balances the weight, the net force is zero, and the elevator can move upward or downward with constant velocity.

Hence, Statement I is true.

The force exerted by the floor on the person is the normal reaction $N$ .

If the elevator goes down with increasing speed, then its acceleration is downward.

Take upward as positive. For the person: $N - mg = -ma$

So, $N = mg - ma = m(g-a)$

Since $a>0$ , $N < mg$

Thus, the floor exerts a force less than the person’s weight, not more.

Hence, Statement II is false.

Therefore, the correct option is: $\boxed{\text{D}}$

Stored correct answer: $\text{D}$

My derived answer: $\text{D}$

They match.