A large tank filled with water to a height ‘h’ is to be emptied through a small hole at the bottom. The ratio of time taken for the level of water to fall from h to $\frac{\mathrm{h}}{2}$ and from $\frac{\mathrm{h}}{2}$ to zero is

(a) $\sqrt{2}$                                               (b) $\frac{1}{\sqrt{2}}$

(c) $\sqrt{2}-1$                                          (d) $\frac{1}{\sqrt{2}-1}$

Concept Questions :-

Bernoulli theorem
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A cylinder of height 20 m is completely filled with water. The velocity of efflux of water (in m/s) through a small hole on the side wall of the cylinder near its bottom is
(a) 10                                        (b) 20
(c) 25.5                                     (d) 5

Concept Questions :-

Bernoulli theorem
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There is a hole in the bottom of tank having water. If total pressure at bottom is 3 atm () then the velocity of water flowing from hole is

(a)  m/s             (b)  m/s

(c)  m/s                (d) None of these

Concept Questions :-

Bernoulli theorem
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A cylindrical tank has a hole of  in its bottom. If the water is allowed to flow into the tank from a tube above it at the rate of . then the maximum height up to which water can rise in the tank is
(a) 2.5 cm                                              (b) 5 cm
(c) 10 cm                                               (d) 0.25 cm

Concept Questions :-

Bernoulli theorem
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A square plate of 0.1 m side moves parallel to a second plate with a velocity of 0.1 m/s, both plates being immersed in water. If the viscous force is 0.002 N and the coefficient of viscosity is 0.01 poise, distance between the plates in m is

(a) 0.1                              (b) 0.05
(c) 0.005                          (d) 0.0005

Concept Questions :-

Viscosity
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Spherical balls of radius 'r' are falling in a viscous fluid of viscosity '$\mathrm{\eta }$' with a velocity 'v'. The retarding viscous force acting on the spherical ball is

(a) Inversely proportional to 'r' but directly proportional to velocity 'v'

(b) Directly proportional to both radius 'r' and velocity 'v'

(c) Inversely proportional to both radius 'r' and velocity 'v'

(d) Directly proportional to 'r' but inversely proportional to 'v'

Concept Questions :-

Viscosity
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A small sphere of mass m is dropped from a great height. After it has fallen 100 m, it has attained its terminal velocity and continues to fall at that speed. The work done by air friction against the sphere during the first 100 m of fall is

(a) Greater than the work done by air friction in the second 100 m

(b) Less than the work done by air friction in the second 100 m

(c) Equal to 100 mg

(d) Greater than 100 mg

Concept Questions :-

Viscosity
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Two drops of the same radius are falling through air with a steady velocity of 5 cm per sec. If the two drops coalesce, the terminal velocity would be

(a) 10 cm per sec                                  (b) 2.5 cm per sec
(c) $5×\left(4{\right)}^{1}{3}}$ cm per sec                          (d) $5×\sqrt{2}$ cm per sec

Concept Questions :-

Surface tension
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A ball of radius r and density $\mathrm{\rho }$ falls freely under gravity through a distance h before entering water. Velocity of ball does not change even on entering water. If viscosity of water is $\mathrm{\eta }$, the value of h is given by

(a) $\frac{2}{9}{\mathrm{r}}^{2}\left(\frac{1-\mathrm{\rho }}{\mathrm{\eta }}\right)\mathrm{g}$

(b) $\frac{2}{81}{\mathrm{r}}^{2}\left(\frac{\mathrm{\rho }-1}{\mathrm{\eta }}\right)\mathrm{g}$

(c) $\frac{2}{81}{\mathrm{r}}^{4}{\left(\frac{\mathrm{\rho }-1}{\mathrm{\eta }}\right)}^{2}\mathrm{g}$

(d) $\frac{2}{9}{\mathrm{r}}^{4}{\left(\frac{\mathrm{\rho }-1}{\mathrm{\eta }}\right)}^{2}\mathrm{g}$

Concept Questions :-

Viscosity
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The rate of steady volume flow of water through a capillary tube of length 'l' and radius 'r' under a pressure difference of P is V. This tube is connected with another tube of the same length but half the radius in series. Then the rate of steady volume flow through them is (The pressure difference across the combination is P)

(a) $\frac{\mathrm{V}}{16}$                                     (b) $\frac{\mathrm{V}}{17}$

(c) $\frac{16\mathrm{V}}{17}$                                    (d) $\frac{17\mathrm{V}}{16}$

Concept Questions :-

Viscosity
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Difficulty Level: