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MCQEasyJEE 2023Newton's Second Law & Force

JEE Physics 2023 Question with Solution

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

    Statement I is true but Statement II is false

  • C

    Both Statement I and Statement II are true

  • D

    Statement I is false but Statement II is true

Answer

Correct answer:B

Step-by-step solution

Standard Method

Given: Two statements about the motion of an elevator and the force exerted by the floor on a person.

Find: Which statement is true and which statement is false.

For Statement-I, when the elevator moves with uniform speed, its acceleration is zero. Therefore, the net force on the elevator is zero, so the tension equals its weight.

T=FgT = F_g

Hence, Statement-I is true.

For Statement-II, when the elevator goes downward with increasing speed, the acceleration is downward. For a person standing inside, weight acts downward and normal reaction acts upward. The force balance is

W−N=Wg×aW - N = \frac{W}{g} \times a

So,

N=W(1−ag)N = W\left(1 - \frac{a}{g}\right)

Since a>0a > 0, we get N<WN < W. Therefore, the force exerted by the floor is less than the person's weight, not more.

Hence, Statement-II is false.

Therefore, the correct option is B.

Statement-wise Explanation

Given: An elevator can move upward or downward, and we must judge two statements using Newton's laws.

Find: The correct option among the four choices.

  1. Statement-I
  • Uniform speed means constant velocity.
  • Therefore, acceleration is zero.
  • By Newton's second law, zero acceleration implies zero net force.
  • So the upward tension must balance the downward weight.
T=WT = W

Thus, Statement-I is true.

  1. Statement-II
  • If the elevator is moving downward with increasing speed, its acceleration is downward.
  • For the person inside the elevator, the forces are:
  • weight WW downward
  • normal reaction NN upward
  • Taking downward direction as the direction of acceleration,
W−N=maW - N = ma

Using W=mgW = mg,

m=Wgm = \frac{W}{g}

Substitute into the equation:

W−N=WgaW - N = \frac{W}{g}a

Rearranging,

N=W−WgaN = W - \frac{W}{g}aN=W(1−ag)N = W\left(1 - \frac{a}{g}\right)

This clearly shows that the normal reaction is smaller than the weight.

Therefore, Statement-II is false.

So, the final conclusion is: Statement I is true but Statement II is false, hence the correct option is B.

Common mistakes

  • Assuming that downward motion always means the normal force is greater than weight. This is wrong because the result depends on the direction of acceleration, not merely motion. For downward increasing speed, acceleration is downward and the normal force becomes less than the weight.

  • Confusing uniform speed with changing speed. Uniform speed means zero acceleration, so net force must be zero. Therefore, the tension balances the weight in Statement-I.

  • Using the wrong force equation sign convention for the person in the elevator. If downward acceleration is taken, then weight and normal force must be written consistently as W−N=maW - N = ma. An inconsistent sign choice leads to the wrong conclusion.

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