JEE Advance - Physics (2014 - Paper 2 Offline - No. 3)
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 d 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 options given below the lists.
| List - I | List - II |
|---|---|
| P. Lift is accelerating vertically up. | 1. d=1.2 m |
| Q. Lift is accelerating vertically down with an acceleration less than the gravitational acceleration. |
2. d > 1.02 m |
| R. Lift is moving vertically up with constant speed. |
3. d < 1.2 m |
| S. Lift is falling freely. | 4. No water leaks out of the jar |
Explanation
The velocity of the efflux depends on the hydrostatic pressure difference and its given by
$$v = \sqrt {2{g_{eff}}H} $$.
After comin gout the jar, water follows the projectile motion. Time taken in traversing a vertical distance h is
$$t = \sqrt {2h/{g_{eff}}} $$.
The horizontal distance covered in this time is
$$d = vt = \sqrt {2{g_{eff}}H} \sqrt {2h/{g_{eff}}} = 2\sqrt {Hh} $$,
which is independent of geff. In the case of free fall, hydrostatic pressure difference is zero (geff = 0) and hence the water does not come out.
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