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 Multiple Choice QuestionsMultiple Choice Questions

1.

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities d1 and d2 are filled in the tube. Each liquid subtends 90o angle at centre. Radius joining their interface makes an angle α with vertical. ratio d1/d2 is

  • fraction numerator 1 plus sin space straight alpha over denominator 1 minus sin space straight alpha end fraction
  • fraction numerator 1 plus space cosα over denominator 1 minus cosα end fraction
  • fraction numerator 1 plus space tan space straight alpha over denominator 1 minus tan space straight alpha end fraction
  • fraction numerator 1 plus cos space straight alpha over denominator 1 minus cos space straight alpha end fraction

C.

fraction numerator 1 plus space tan space straight alpha over denominator 1 minus tan space straight alpha end fraction
straight P subscript straight A space equals space straight P subscript straight B
straight P subscript 0 space plus space straight d subscript 1 straight g end subscript straight R space left parenthesis Cos space straight alpha space minus sin space straight alpha right parenthesis space equals straight P subscript 0 space plus straight d subscript 2 straight R space left parenthesis Cos space straight alpha plus sin space straight alpha right parenthesis
rightwards double arrow space straight d subscript 1 over straight d subscript 2 space equals space fraction numerator cos space straight alpha space plus sin space straight alpha over denominator cos space straight alpha minus sin space straight alpha end fraction space equals space fraction numerator 1 plus space tan space straight alpha over denominator 1 minus space tanα end fraction
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2.

A spherical solid ball of volume V is made of a material of density ρ1. It is falling through a liquid of density ρ221). Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed v, i.e., Fviscous = −kv2 (k>0). The terminal speed of the ball is

  • square root of fraction numerator Vg left parenthesis straight rho subscript 1 minus straight rho subscript 2 right parenthesis over denominator straight k end fraction end root
  • Vgρ subscript 1 over straight k
  • square root of Vgρ subscript 1 over straight k end root
  • fraction numerator Vg left parenthesis straight rho subscript 1 minus straight rho subscript 2 right parenthesis over denominator straight k end fraction

A.

square root of fraction numerator Vg left parenthesis straight rho subscript 1 minus straight rho subscript 2 right parenthesis over denominator straight k end fraction end root

ρ1Vg − ρ2Vg = kv2T

rightwards double arrow space straight V subscript straight T space equals space square root of fraction numerator Vg space left parenthesis straight rho subscript 1 minus straight rho subscript 2 right parenthesis over denominator straight k end fraction end root

442 Views

3.

A jar filled with two non-mixing liquids 1 and 2 having densities ρ1 and ρ2 respectively. A solid ball, made of a material of density ρ3, is dropped in the jar. It comes to equilibrium in the position shown in the figure.
Which of the following is true for ρ1, ρ2 and ρ3?

  • ρ3 < ρ1 < ρ2

  • ρ1 < ρ3 < ρ2

  • ρ1 < ρ2 < ρ3

  • ρ1 < ρ3 < ρ2


D.

ρ1 < ρ3 < ρ2



As liquid 1 floats above liquid 2,
ρ1 < ρ2
The ball is unable to sink into liquid 2, ρ3 < ρ2
The ball is unable to rise over liquid 1
ρ1 < ρ3 Thus, ρ1 < ρ3 < ρ2

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4.

The following observations were taken for determining surface tension T of water by the capillary method :
Diameter of capillary, D = 1.25 × 10–2 m rise of water, h = 1.45 × 10–2 m
Using g = 9.80 m/s2 and the simplified relation T = (rhg/2) x103 n/m, the possible error in surface tension is closest to:

  • 2.4%

  • 10%

  • 0.15%

  • 1.5%


D.

1.5%

straight T space equals space rhg over 2 space straight x space 10 cubed
fraction numerator increment straight T over denominator straight T end fraction space equals space fraction numerator increment straight r over denominator straight r end fraction space plus space fraction numerator increment straight h over denominator straight h end fraction space plus 0
100 space straight x space fraction numerator increment straight T over denominator straight T end fraction space equals space open parentheses fraction numerator 10 to the power of negative 2 end exponent space straight x space.01 over denominator 1.25 space straight x space 10 to the power of negative 2 end exponent end fraction space plus fraction numerator 10 to the power of negative 2 end exponent space straight x space 0.1 over denominator 1.45 space straight x space 10 to the power of negative 2 end exponent end fraction close parentheses 100
space equals space 0.8 space plus 0.689
equals space 1.489
space 100 space straight x space fraction numerator increment straight T over denominator straight T end fraction space equals space 1.489 percent sign
space approximately equal to space 1.5 space percent sign
1509 Views

5.

A capillary tube (A) is dropped in water. Another identical tube (B) is dipped in a soap water solution.Which of the following shows the relative nature of the liquid columns in the two tubes? 


C.

Capillary rise h = 2T cosθ /ρgr. As soap solution has lower T, h will be low. 

796 Views

6.

On the heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be spheres of radius R and making a circular contact of radius r with the bottom of the vessel. If r < < R and the surface tension of water is T, value of r just before bubbles detach is (density of water is ρw)

  • straight R squared square root of fraction numerator 2 straight rho subscript straight w straight g over denominator 3 straight T end fraction end root
  • straight R squared square root of fraction numerator straight rho subscript straight w straight g over denominator 6 straight T end fraction end root
  • straight R squared square root of fraction numerator straight rho subscript straight w straight g over denominator straight T end fraction end root
  • straight R squared space square root of fraction numerator 3 straight rho subscript straight w straight g over denominator straight T end fraction end root

A.

straight R squared square root of fraction numerator 2 straight rho subscript straight w straight g over denominator 3 straight T end fraction end root

The bubble will detach if, 
Buoyant force ≥ Surface tension force

4 over 3 πR cubed straight rho subscript straight w straight g space greater or equal than integral straight T space straight x space dl space sin space straight theta space


left parenthesis straight rho subscript straight w right parenthesis open parentheses 4 over 3 πR cubed close parentheses straight g greater or equal than left parenthesis straight T right parenthesis left parenthesis 2 πpr right parenthesis space sin space straight theta
sin space straight theta space equals space straight r over straight R
solving space straight r space equals space square root of fraction numerator 2 straight p subscript straight w straight R to the power of 4 straight g over denominator 3 straight T end fraction end root space equals space straight R squared square root of fraction numerator 2 straight rho subscript straight w straight g over denominator 3 straight T end fraction end root

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7.

Water is flowing continuously from a tap having an internal diameter 8 × 10-3 m. The water velocity as it leaves the tap is 0.4 ms-1. The diameter of the water stream at a distance 2 × 10-1 m below the tap is close
to:

  • 7.5 x 10-3 m

  • 9.6x 10-3 m

  • 3.6x 10-3 m

  • 5.0x 10-3 m


C.

3.6x 10-3 m

From Bernoulli's theorem
ρgh space equals space 1 half straight rho left parenthesis straight v subscript 2 superscript 2 minus straight v subscript 1 superscript 2 right parenthesis
gh space equals space 1 half straight v subscript 1 superscript 2 space open parentheses open parentheses straight v subscript 2 over straight v subscript 1 close parentheses minus 1 close parentheses space left parenthesis therefore straight A subscript 1 straight v subscript 1 space equals straight A subscript 2 straight v subscript 2 right parenthesis
rightwards double arrow space space open parentheses straight A subscript 1 over straight A subscript 2 close parentheses squared space equals space 1 space plus space fraction numerator 2 hg over denominator straight v subscript 1 superscript 2 end fraction
rightwards double arrow open parentheses straight D subscript 1 over straight D subscript 2 close parentheses to the power of 4 space equals space 1 space plus space fraction numerator 2 gh over denominator straight v subscript 1 superscript 2 end fraction
rightwards double arrow space straight D subscript 2 space equals space straight D subscript 1 over open parentheses 1 plus begin display style fraction numerator 2 gh over denominator straight v subscript 1 superscript 2 end fraction end style close parentheses to the power of 1 divided by 4 end exponent space equals space fraction numerator 8 space straight x space 10 to the power of negative 3 end exponent over denominator open parentheses begin display style fraction numerator 1 plus space 2 space straight x space 10 space straight x 0.2 over denominator left parenthesis 0.4 right parenthesis squared end fraction end style close parentheses to the power of 1 divided by 4 end exponent end fraction
space equals space 3.6 space straight x space 10 to the power of negative 3 end exponent space straight m

494 Views

8.

An open glass tube is immersed in mercury in such a way that a length of 8 cm extends above the mercury level. The open end of the tube is then closed and sealed and the tube is raised vertically up by additional 46 cm. What will be the length of the air column above mercury in the tube now? (Atmospheric pressure = 76 cm of Hg)

  • 16 cm

  • 22 cm

  • 38 cm

  • 6 cm


A.

16 cm

Since the system is accelerating horizontally such that no component of acceleration in the vertical direction. Hence, the pressure in the vertical direction will remain unaffected.

straight p subscript 1 space equals straight p subscript 0 space plus ρgh

.
For air trapped in tube, p1V1 = p2V2
p1 = patm = pg76
V1 = A.8 [ A = area of cross section]
p2 = patm - ρg(54-x) =  ρg(22+x)
V2 = A.x
ρg76 x 8A = ρg (22+x) Ax
x2+22x-78x 8
by solving, x = 16

668 Views

9.

A ball is made of a material of density ρ where ρoil < ρ < ρwater with ρoil and ρwater representing the densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, which of the following pictures represents its equilibrium position?


C.

 ρoil < ρ < ρwater 
Oil is the least dense of them, so it should settle at the top with water at the base. Now, the ball is denser than oil but less denser than water. So, it will sink through oil but will not sink in water. So, it will stay at the oil -water interface.

443 Views

10.

If the terminal speed of a sphere of gold (density = 19.5 kg/m3 ) is 0.2 m/s in a viscous liquid (density = 1.5 kg/m3 ) of the same size in the same liquid.

  • 0.2 m/s

  • 0.4 m/s

  • 0.133 m/s

  • 0.1m/s


D.

0.1m/s

straight V subscript straight s over straight V subscript straight g space equals space fraction numerator left parenthesis straight p subscript straight s minus straight p subscript calligraphic l right parenthesis over denominator left parenthesis straight rho subscript straight g minus straight rho subscript calligraphic l right parenthesis end fraction
straight v subscript straight s space equals space 0.1 space straight m divided by straight s
483 Views