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A soap bubble , having radius of 1 mm is blown from, a detergent solution having a surface tension , of 2.5 \times 10 ^{-2 } N/m. The pressure inside the bubble equals at a point Z_0 below  the free surface of water in a container of water = 10 ^ 3 Kg / m ^ 3 , the value of Z_0 is 

  • Option 1)

    100 cm 

  • Option 2)

    10 cm 

  • Option 3)

    1 cm 

  • Option 4)

    0.5 cm 

GIVEN : surface tension = force /length = 0.025 N/m

radius = 1mm = 0.001m

p(final) - p(initial) = 4t/r

where z is a pressure inside the bubble 

p(z=final) - p(initial) =pgh =pgz = 4t/r

pgz = 4t/r

z = 4t/pgr

z = 4(0.025)/(0.001)(1000)(10)

z =0.100/10

z = 0.100(0.1)

z = 0.01

z= 1(0.01)

z=1cm

option 3) 1cm

 

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The unit of thermal conductivity is : 

  • Option 1)

    JmK^{-1}

  • Option 2)

    Jm^{-1}K^{-1}

  • Option 3)

    WmK^{-1}

  • Option 4)

    Wm^{-1}K^{-1}

Option 1)Option 2)Option 3)Option 4)

A small hole of area of cross sectyion 2 mm ^ 2 is  present mear the botom  of a fully  filled open tank  of heiht 2 m . Taking g = 10 m /s ^2 , the rate of flow of water through the open hole would be nearly : 

 

  • Option 1)

    12.6 \times 10 ^{-6 } m^3 / s

  • Option 2)

    8.9 \times 10 ^{-6 } m^3 / s

  • Option 3)

    2.23 \times 10 ^{-6 } m^3 / s

  • Option 4)

    6.4 \times 10 ^{-6 } m^3 / s

 
  Option 1) Option 2) Option 3) Option 4)

When a block of mass M is suspended by a long wire of length L , The length of the wire becomes (L+l ) . The elastic potential energy stored in the extended wire is : 

 

  • Option 1)

    Mgl 

  • Option 2)

    MgL 

  • Option 3)

    1/2 Mgl

  • Option 4)

    1/ MgL

 Option 1)Mgl Option 2)MgL Option 3)1/2 MglOption 4)1/ MgL

A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in temprature . The length  of aluminium rod is : 

(^\alpha C_u = 1.7 \times 10 ^{-5} K^{-1} \: \: and \: \: ^ \alpha A1 = 2.2 \times 10 ^{-5}K^{-1})

  • Option 1)

    6.8 cm 

  • Option 2)

    113.9 cm 

  • Option 3)

    88 cm 

  • Option 4)

    68 cm 

 
For Copper  L = 88 cm    Option 1) 6.8 cm  Option 2) 113.9 cm  Option 3) 88 cm  Option 4) 68 cm 
Medical
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A body cools from a temperature 3T to 2T in 10 minutes. The room temperature is T. Assume that Newton's law of cooling is applicable. The temperature of the body at the end of next 10 minutes will be

  • Option 1)

    \frac{7} {4}T

  • Option 2)

    \frac{3} {2}T

  • Option 3)

    \frac{4} {3}T

  • Option 4)

    T

 
As we learnt in When body Cools by Radiation from theta1 degree c to theta two degree c in time t - - wherein       From newton's law of cooling  Let us say temperature after 10 minutes become T1 Then    Option 1) This solution is incorrect  Option 2) This solution is correct  Option 3) This solution is incorrect  Option 4) T This solution is incorrect 
Medical
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A black body is at a temperature of 5760 K. The energy of radiation emitted by the body at wavelength 250 nm is U1,  at wavelength 500 nm is U2 and that at 1000 nm is U3. Wien's constant, b = 2.88 \times 106 nmK. Which of the following is correct?

  • Option 1)

    U1 = 0

  • Option 2)

    U3 = 0

  • Option 3)

    U1 > U2

  • Option 4)

    U2 > U1

 
As discussed Stefan's Law - Radiant energy emitted by a perfectly black body per unit area per sec is directly proportional to 4th power of temperature of the body. -     Hence energy radiated at 500nm is maximum  Option 1) U1 = 0 This option is incorrect  Option 2) U3 = 0 This option is incorrect  Option 3) U1 > U2 This option is incorrect  Option 4) U2 > U1 This option is correct 
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