Fluid Mechanics PYQs Set 5 (PDF)

Set 5 of 10 · Questions 121-150 of 289

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Mere Teacher · Previous Year Questions JEE Main Physics · Fluid Mechanics · Set 5 (Q121-150)
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121. $When a part of a straight capillary tube is placed vertically in a liquid, the liquid raises upto certain height h . If the inner radius of the capillary tube, density of the liquid and surface tension of the liquid decrease by 1 % each, then the height of the liquid in the tube will change by % .$ (1) $+1$ (2) $-3$ (3) $+3$ (4) $-1$ 122. $Water from a pipe is coming at a rate of 100 liters per minute. If the radius of the pipe is 5 cm, the Reynolds number for the flow is of the order of: (density of water =1000 kg/m³, coefficient of viscosity of water =1 mPa s).$ (1) $10^{3}$ (2) $10^{4}$ (3) $10^{2}$ (4) $10^{6}$ 123. $Water rises to height h in a capillary tube. If the length of capillary tube above the surface of water is made less than h, then$ (1) $water rises upto the top of capillary tube and stays there without overflowing$ (2) $water rises upto a point a little below the top and stays there$ (3) $water does not rise at all.$ (4) $water rises upto the tip of capillary tube and then starts overflowing like fountain.$ 124. $A small ball of mass m and density ρ is dropped in a viscous liquid of density ρ_{0} . After sometime, the ball falls with constant velocity. The viscous force on the ball is:$ (1) $mg (1 - ρ ρ_{0})$ (2) $mg (1 + \frac{ρ}{ρ _{0}})$ (3) $mg (\frac{ρ _{0}}{ρ} - 1)$ (4) $mg (1 - \frac{ρ _{0}}{ρ})$ 125. $Two capillary tubes of different diameters are dipped in water. The rise of water is$ (1) $the same in both tubes$ (2) $greater in the tube of larger diameter$ (3) $greater in the tube of smaller diameter$ (4) $independent of the diameter of the tube.$ 126. $The heart of man pumps 5 liters of through the arteries per minute at a pressure of 150 mm of mercury. If the density of mercury be 13.6 \times 1 0^{3} kg/ m^{3} and g = 10m/ s^{2} then the power of heart in watt is:$ (1) $2.35$ (2) $3.0$ (3) $1.50$ (4) $1.70$ 127. $The lower end of a capillary tube is dipped into water and it is observed that the water in capillary tube rises by 7.5 cm . Find the radius of the capillary tube used, if surface tension of water is 7.5 \times 10^{- 2} Nm^{- 1} . Angle of contact between water and glass is 0^{\circ} and acceleration due to gravity is 10 ms^{- 2} .$ (1) $0.2 cm$ (2) $0.1 cm$ (3) $0.4 mm$ (4) $0.2 mm$ 128. $An air bubble of volume 1 c m^{3} rises from the bottom of a lake 40 m deep to the surface at a temperature of 12 °C. The atmospheric pressure is 1 x 1 0^{5} Pa, the density of water is 1000 kg m^{- 3} and g = 10 m s^{- 2} . There is no difference of the temperature of water at the depth of 40 m and on the surface. The volume of air bubble when it reaches the surface will be$ (1) $2 c m^{3}$ (2) $3 c m^{3}$ (3) $4 c m^{3}$ (4) $5 c m^{3}$ 129. $A cylinder of mass and material density ρ hanging from a string is lowered into a vessel of cross-sectional area A containing a liquid of density σ (< ρ) until it is fully immersed. The increase in pressure at the bottom of the vessel is$ (1) $Zero$ (2) $\frac{mg}{A}$ (3) $\frac{mgρ}{σA}$ (4) $\frac{mσg}{ρA}$ 130. $An object of mass m is suspended at the end of a massless wire of length L and area of cross-section, A. Young modulus of the material of the wire is Y . If the mass is pulled down slightly its frequency of oscillation along the vertical direction is$ (1) $f = \frac{1}{2 π} \frac{mL}{YA}$ (2) $f = \frac{1}{2 π} \frac{YA}{mL}$ (3) $f = \frac{1}{2 π} \frac{YL}{mA}$ (4) $f = \frac{1}{2 π} \frac{mA}{YL}$ 131. $Eight equal drops of water are falling through air with a steady velocity of 10 cm s^{- 1} . If the drops combine to form a single drop big in size, then the terminal velocity of this big drop is$ (1) $40 cm s^{- 1}$ (2) $10 cm s^{- 1}$ (3) $30 cm s^{- 1}$ (4) $80 cm s^{- 1}$ 132. $Two different wires having lengths L_{1} and L_{2}, and respective temperature coefficient of linear expansion α_{1} and α_{2} are joined end-to-end. Then the effective temperature coefficient of linear expansion is$ (1) $2 α_{1} α_{2}$ (2) $4 \frac{α _{1} α _{2}}{α _{1} + α _{2}} \frac{L _{2} L _{1}}{( L _{2} + L _{1} ) ^{2}}$ (3) $\frac{α _{1} + α _{2}}{2}$ (4) $\frac{α _{1} L _{1} + α _{2} L _{2}}{L _{1} + L _{2}}$ 133. $A cylindrical metal box whose flat surface has an area of 0.01 m^{2} rests on liquid of 0.3 mm thickness. If upon applying a horizontal force of magnitude \frac{1}{3} N, the box slides with a constant speed of 0.09 ms^{- 1}, the coefficient of viscosity of the liquid is nearly$ (1) $2.5\times 1 0^{- 2} Pa.s$ (2) $1.1\times 1 0^{- 1} Pa.s$ (3) $1.1\times 1 0^{- 2} Pa.s$ (4) $2.5\times 1 0^{- 1} Pa.s$ 134. $When the temperature of a metal wire is increased from 0^{\circ} C to 10^{\circ} C its length increases by 0.02 % The percentage change in its mass density will be closest to$ (1) $2.3$ (2) $0.06$ (3) $0.8$ (4) $0.008$ 135. $Water does not wet an oily glass because$ (1) $cohesive force of oil is greater than adhesive force between oil and glass$ (2) $cohesive force of oil is greater than cohesive force of water$ (3) $oil repels water$ (4) $cohesive force of water is greater than adhesive force between water and oil molecules$ 136. $Energy needed in breaking a liquid drop of radius R, into n smaller drops each of radius r, is [T- Surface tension of the liquid]$ (1) $(4 π r^{2} n - 4 π R^{2}) T$ (2) $(\frac{4}{3} π r^{3} n - \frac{4}{3} π R^{3}) T$ (3) $(4 π R^{2} - 4 π r^{2}) nT$ (4) $(4 π R^{2} - n 4 π r^{2}) / T$ 137. $The top of a water tank is open to air and its water level is maintained. It is giving out 0.74 m^{3} / min. water per minute through a circular opening of 2 cm radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to:$ (1) $2.9 m$ (2) $9.6 m$ (3) $4.8 m$ (4) $6.0 m$ 138. $A metal cube of side 10 cm rests on a film of a liquid of thickness 0.2 mm . If upon applying a horizontal force F of magnitude 0.1 N the cube slides with a constant speed of 0.08 m / s, then the coefficient of viscosity is$ (1) $2.5 \times 1 0^{- 2} Ns m^{- 2}$ (2) $0.25 \times 1 0^{- 2} Ns m^{- 2}$ (3) $5 \times 1 0^{- 2} Ns m^{- 2}$ (4) $0.5 \times 1 0^{- 2} Ns m^{- 2}$ 139. $A small spherical ball of radius r, falling through a viscous medium of negligible density has terminal velocity ' v'. Another ball of the same mass but of radius 2 r, falling through the same viscous medium will have terminal velocity:$ (1) $\frac{v}{2}$ (2) $\frac{v}{4}$ (3) $4 v$ (4) $2 v$ 140. $A 20 g copper block is suspended by a vertical spring causing 1 cm elongation over the natural length of spring. If a beaker of water is placed below the block so that the copper block is completely immersed in the liquid, the elongation of the spring is (Density of copper 9000 kg m^{- 3}, Density of water 1000 kg m^{- 3}, g = 10 ms^{- 2})$ (1) $0.25 cm$ (2) $0.15 cm$ (3) $0.78 cm$ (4) $0.89 cm$ 141. $A soap bubble of radius 1.0 cm is formed inside another soap bubble of radius 2.0 cm . The radius of an another soap bubble which has the same pressure difference as that between the inside of the smaller and outside of large soap bubble, in meters is$ (1) $6.67 \times 10^{- 3}$ (2) $3.34 \times 10^{- 3}$ (3) $2.23 \times 10^{- 3}$ (4) $4.5 \times 10^{- 3}$ 142. $If a vessel containing a fluid of density ρ upto height h is accelerated vertically downwards with acceleration a_{0} . Then, the pressure by fluid at the bottom of vessel is given by the equation .............. (p_{0} denotes the atmospheric pressure and g denotes the acceleration due to gravity).$ (1) $p = p_{0} + ρgh + ρh a_{0}$ (2) $p = p_{0} + ρgh$ (3) $p = p_{0} + ρh (g - a_{0})$ (4) $p = p_{0} - ρgh$ 143. $In an experiment to verify Stokes law, a small spherical ball of radius r and density ρ falls under gravity through a distance h in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value of h is proportional to (ignore viscosity of air)$ (1) $r^{4}$ (2) $r^{3}$ (3) $r$ (4) $r^{2}$ 144. $A water drop breaks into 64 identical droplets of each surface area 10^{- 7} m^{2} . If the surface tension of water is 0.07 Nm^{- 1}, the increase in the surface energy in the process is$ (1) $158 \times 10^{- 9} J$ (2) $432 \times 10^{- 9} J$ (3) $216 \times 10^{- 9} J$ (4) $336 \times 10^{- 9} J$ 145. $A thin transparent film with refractive index 1.4, is held on circular ring of radius 1.8 cm.The fluid in the film evaporates such that transmission through the film at wavelength 560 nm goes to a minimum every 12 seconds. Assuming that the film is flat on its two sides, the rate of evaporation is.$ 146. $When a long glass capillary tube of radius 0.015 cm is dipped in a liquid, the liquid rises to a height of 15 cm within it. If the contact angle between the liquid and glass to close to 0^{\circ} the surface tension of the liquid, in milliNewton m^{- 1}, is [ρ_{(liquid)} = 900 kgm^{- 3}, g = 10 ms^{- 2}] (Give answer in closest integer) \dots\dots\dots\dots\dots..$ 147. $A liquid column of height 0.04 cm balances excess pressure of a soap bubble of certain radius. If density of liquid is 8 \times 10^{3} kg m^{- 3} and surface tension of soap solution is 0.28 Nm^{- 1}, then diameter of the soap bubble is ______cm . (if g = 10 m s^{- 2})$ 148. $A big drop is formed by coalescing 1000 small identical drops of water. If E_{1} be the total surface energy of 1000 small drops of water and E_{2} be the surface energy of single big drop of water, the E_{1} : E_{2} is x : 1 where x =_______$ 149. $When a rubber ball is taken to a depth of ....m in deep sea, its volume decreases by 0.5%. (The bulk modulus of rubber = 9.8 \times 1 0^{8} N m^{- 2} Density of sea water = 1 0^{3} k g m^{- 3} g = 9.8 m / s^{2})$ 150. $The velocity of upper layer of water in a river is 36 k m l r^{1} . Shearing stress between horizontal layers of water is 1 0^{- 3} N m^{- 2} . Depth of the river is__________m. (Co-efficiency of viscosity of water is 1 0^{- 2} Pa.s)$