Sixty four spherical rain drops of equal size are falling vertically through air with a terminal velocity 1.5 ms^-1 . If these drops coalesce to form a big spherical drop, then terminal velocity of big drop is

• 8 ms^-1

• 16 ms^-1

• 24 ms^-1

• 32 ms^-1

A cylinder of height 20 m is completely filled with water. The velocity of efflux of water (in ms^-1 ) through a hole on the side wall of the cylinder near its bottom, is

• 10

• 20

• 25.5

• 5

A liquid flows through a pipe of non-uniform cross-section. If A₁ and A₂ are the cross-sectional areas of the pipe at two points, the ratio of velocities of the liquid at these points will be

• A₁A₂

• $\frac{{\mathrm{A}}_1}{{\mathrm{A}}_2}$

• $\frac{{\mathrm{A}}_2}{{\mathrm{A}}_1}$

• $\frac{1}{{\mathrm{A}}_1{\mathrm{A}}_2}$

A piece of ice is floating in a jar containing water. When the ice melts, then the level of water

• rises

• falls

• remains unchanged

• rises or falls

Radius of an air bubble at the bottom of the lake is r and it becomes 2 r when the air bubble rises to the top  surface of the lake. If P cm of water be the atmospheric pressure, then the depth ofthe lake is

• 2 P

• 8 P

• 4 P

• 7 P

A manometer connected to a closed tap reads 4.5 x 10⁵ Pa. When the tap is opened the  reading of the manometer falls to 4 x 10⁵ Pa. Then the velocity of flow of water is

• 7 ms^-1

• 8 ms^-1

• 9 ms^-1

• 10 ms^-1

A beaker of radius 15 cm is filled with a liquid of surface tension 0.75 N/m. Force across an imaginary diameter on the surface of the liquid is

• 0.075 N

• 1.5 × 10^-2 N

• 0.225 N

• 2.25 × 10^-2 N

Two spheres of equal masses but radii r₁ and r₂ are allowed to fall in a liquid of infinite column. The ratio of their terminal velocities is

• 1

• r₁ : r₂

• r₂ : r₁

• $\sqrt{{\mathrm{r}}_1} : \sqrt{{\mathrm{r}}_2}$

A liquid flows through two capillary tubes A and B connected in series. The length and radius of B are twice those of A. What is the ratio of the pressure difference across A to that across B ?

n identical droplets are charged to V volt  each. if they coalesce to form a single drop, then its potential will be

• n^2/3V

• n^1/3V

• nV

• V/n