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JEE Advanced 2014 · Paper 2, Physics question 20

A person in a lift is holding a water jar, which has a small hole at the lower end of its side. When the lift is at rest, the water jet coming out of the hole hits the floor of the lift at a distance of 1.2 m from the person. In the following, state of the lift's motion is given in List I and the distance where the water jet hits the floor of the lift is given in List II. Match the statements from List I with those in List II and select the correct answer using the code given below the list.

List I

  • P
    Lift is accelerating vertically up.
  • Q
    Lift is accelerating vertically down with an acceleration less than the gravitational acceleration.
  • R
    Lift is moving vertically up with constant speed.
  • S
    Lift is falling freely.

List II

  • 1
    d=1.2d=1.2 m
  • 2
    d>1.2d>1.2 m
  • 3
    d<1.2d<1.2 m
  • 4
    No water leaks out of the jar
Choose one option
Answer and worked solution

Official answer: C

Effective gravity. In the lift's frame the water feels geff=g±ag_\text{eff}=g\pm a.

Range on the floor. With water height hh above the hole and the hole at height HH above the floor:
v=2geffh,t=2Hgeff,d=vt=2hH.v=\sqrt{2g_\text{eff}h},\qquad t=\sqrt{\frac{2H}{g_\text{eff}}},\qquad d=vt=2\sqrt{hH}.
geffg_\text{eff} cancels.

  • P accelerating up: d=1.2d=1.2 m → 1.
  • Q accelerating down with a<ga<g: d=1.2d=1.2 m → 1.
  • R constant velocity: geff=gg_\text{eff}=g, d=1.2d=1.2 m → 1.
  • S free fall: geff=0g_\text{eff}=0, there is no pressure to push water out → 4.

(C) P → 1, Q → 1, R → 1, S → 4

Topics:Bernoulli's principlePseudo forces and non-inertial framesProjectile motion
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