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
Four charges Q1, Q2, Q3 and Q4 of same magnitude are fixed along the x axis at x = $$-$$2a, $$-$$a, +a and +2a, respectively. A positive charge q is placed on the positive y axis at a distance b > 0. Four options of the signs of these charges are given in List I. The direction of the forces on the charge q is given in List II. Match List I with List II and select the correct answer using the code given below the lists.
| List I | List II | ||
|---|---|---|---|
| P. | Q$$_1$$, Q$$_2$$, Q$$_3$$, Q$$_4$$ all positive | 1. | +x |
| Q. | Q$$_1$$, Q$$_2$$ positive; Q$$_3$$, Q$$_4$$ negative | 2. | $$ - $$x |
| R. | Q$$_1$$, Q$$_4$$ positive; Q$$_2$$, Q$$_3$$ negative | 3. | +y |
| S. | Q$$_1$$, Q$$_3$$ positive; Q$$_2$$, Q$$_4$$ negative | 4. | $$ - $$y |
Four combinations of two thin lenses are given in List I. The radius of curvature of all curved surfaces is r and the refractive index of all the lenses is 1.5. Match lens combinations in List I with their focal length in List II and select the correct answer using the code given below the lists.
A block of mass m1 = 1 kg another mass m2 = 2 kg, are placed together (see figure) on an inclined plane with angle of inclination $$\theta$$. Various values of $$\theta$$ are given in List I. The coefficient of friction between the block m1 and the plane is always zero. The coefficient of static and dynamic friction between the block m2 and the plane are equal to $$\mu$$ = 0.3. In List II expressions for the friction on the block m2 are given. Match the correct expression of the friction in List II with the angles given in List I, and choose the correct option. The acceleration due to gravity is denoted by g.
[Useful information : tan (5.5$$^\circ$$) $$\approx$$ 0.1; tan (11.5$$^\circ$$) $$\approx$$ 0.2; tan (16.5$$^\circ$$) $$\approx$$ 0.3]
| List I | List II | ||
|---|---|---|---|
| P. | $$\theta = 5^\circ $$ |
1. | $${m_2}g\sin \theta $$ |
| Q. | $$\theta = 10^\circ $$ |
2. | $$({m_1} + {m_2})g\sin \theta $$ |
| R. | $$\theta = 15^\circ $$ |
3. | $$\mu {m_2}g\cos \theta $$ |
| S. | $$\theta = 20^\circ $$ |
4. | $$\mu ({m_1} + {m_2})g\cos \theta $$ |