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 |
A glass capillary tube is of the shape of truncated cone with an apex angle $$\alpha$$ so that its two ends have cross sections of different radii. When dipped in water vertically, water rises in it to a height h, where the radius of its cross section is b. If the surface tension of water is S, its density is $$\rho$$, and its contact angle with glass is $$\theta$$, the value of h will be (g is the acceleration due to gravity)
A spray gun is shown in the below figure where a piston pushes air out of a nozzle. A thin tube of uniform cross-section is connected to the nozzle. The other end of the tube is in a small liquid container. As the piston pushes air through the nozzle, the liquid from the container rises into the nozzle and is sprayed out. For the spray gun shown, the radii of the piston and the nozzle are 20 mm and 1 mm, respectively. The upper end of the container is open to the atmosphere.
If the piston is pushed at a speed of 5 mm s$$-$$1, the air comes out of the nozzle with a speed of
A spray gun is shown in the below figure where a piston pushes air out of a nozzle. A thin tube of uniform cross-section is connected to the nozzle. The other end of the tube is in a small liquid container. As the piston pushes air through the nozzle, the liquid from the container rises into the nozzle and is sprayed out. For the spray gun shown, the radii of the piston and the nozzle are 20 mm and 1 mm, respectively. The upper end of the container is open to the atmosphere.
If the density of air is $$\rho$$a and that of the liquid $$\rho$$l, then for a given piston speed the rate (volume per unit time) at which the liquid is sprayed will be proportional to