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 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 lists.
| List I | List II |
|---|---|
| P. Lift is accelerating vertically up. | 1. |
| Q. Lift is accelerating vertically down with an acceleration less than the gravitational acceleration. | 2. |
| R. Lift is moving vertically up with constant speed. | 3. |
| S. Lift is falling freely. | 4. No water leaks out of the jar |
- (A)P-2, Q-3, R-2, S-4
- (B)P-2, Q-3, R-1, S-4
- (C)P-1, Q-1, R-1, S-4✓ Correct
- (D)P-2, Q-3, R-1, S-1
Answer: (C)
Solution
The horizontal range of the water jet is , where (horizontal velocity from Torricelli's theorem) and (time to fall height ).
Thus .
P, Q, R: For any non-zero , the ratio changes but the product and the geometry remain such that stays constant at m (the factors cancel in the derivation). P→1, Q→1, R→1.
S: In free fall, , so there's no pressure difference to push water out. No water leaks. S→4.
Answer: P-1, Q-1, R-1, S-4.
Thus .
P, Q, R: For any non-zero , the ratio changes but the product and the geometry remain such that stays constant at m (the factors cancel in the derivation). P→1, Q→1, R→1.
S: In free fall, , so there's no pressure difference to push water out. No water leaks. S→4.
Answer: P-1, Q-1, R-1, S-4.
JEE Advanced · 2014 · 25 May 2014 · Paper 2 · Single correct option