Question 4

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:

Solution

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 on a person is more than their weight when the elevator goes down with increasing speed.

Evaluation of Statement I:

When the elevator moves with uniform speed (zero acceleration), by Newton's second law: $$T - Mg = 0$$, so $$T = Mg$$. The tension in the cable exactly balances the weight. Statement I is true.

Evaluation of Statement II:

"Going down with increasing speed" means the elevator has a downward acceleration ($$a$$ directed downward).

For a person of mass $$m$$ inside: $$mg - N = ma$$ (taking downward as positive).

$$N = m(g - a)$$

Since $$a > 0$$ (downward acceleration), $$N < mg$$. The normal force is less than the person's weight, not more. Statement II is false.

Statement I is true but Statement II is false, which corresponds to Option 2.

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