6. A fluid is in streamline flow across a horizontal pipe of variable area of cross section. For this which of the following statements is correct?

1. 1. The velocity is minimum at the narrowest part of the pipe and the pressure is minimum at the widest part of the pipe ​
      

   
   
   

   2. The velocity is maximum at the narrowest part of the pipe and pressure is maximum at the widest part of the pipe

   
   
   

   3. Velocity and pressure both are maximum at the narrowest part of the pipe

   
   
   

   4. Velocity and pressure both are maximum at the widest part of the pipe

   
   
   

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1. View Hint View Answer Discuss in Forum

   According to Bernoulli’s theorem,
   

   P -	1	ρ v2 = constant and Av = constant
   	2

   
   If A is minimum, v is maximum, P is minimum.

   Correct Option: B

   According to Bernoulli’s theorem,
   

   P -	1	ρ v2 = constant and Av = constant
   	2

   
   If A is minimum, v is maximum, P is minimum.

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7. The cylindrical tube of a spray pump has radius, R, one end of which has n fine holes, each of radius r. If the speed of the liquid in the tube is V, the speed of the ejection of the liquid through the holes is :​​​

1. 1. 	VR2
      	nr2

   
   
   

   2. 	VR2
      	n3 r2

   
   
   

   3. 	V2R
      	nr

   
   
   

   4. 	VR2
      	n2 r2

   
   
   

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1. View Hint View Answer Discuss in Forum

   Inflow rate of volume of the liquid = Outflow rate of volume of the liquid
   

   πR2V = nπr2(v) ⇒ V =	πR2V	=	VR2
   	nπr2		nr2

   Correct Option: A

   Inflow rate of volume of the liquid = Outflow rate of volume of the liquid
   

   πR2V = nπr2(v) ⇒ V =	πR2V	=	VR2
   	nπr2		nr2

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8. A wind with speed 40 m/s blows parallel to the roof of a house. The area of the roof is 250 m². Assuming that the pressure inside the house is atmosphere pressure, the force exterted by the wind on the roof and the direction of the force will be (ρ_air = 1.2 kg/m³)​​
   

1. 1. 4.8 × 10⁵ N, upwards

   
   
   

   2. 2.4 × 10⁵ N, upwards

   
   
   

   3. 2.4 × 10⁵ N, downwards

   
   
   

   4. 4.8 × 10⁵ N, downwards

   
   
   

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1. View Hint View Answer Discuss in Forum

   According to Bernoulli’s theorem,
   

   P +	1	ρv2 = P0 + 0
   	2

   
   

   So ,​ ∆P =	1	ρv2
   	2

   
   
   

   F = ∆P =	1	ρv2A
   	2

   
   

   =	1	× 1.2 × 40 × 40 × 250
   	2

   
   = 2.4 × 10⁵ N (upwards)
   

   Correct Option: B

   According to Bernoulli’s theorem,
   

   P +	1	ρv2 = P0 + 0
   	2

   
   

   So ,​ ∆P =	1	ρv2
   	2

   
   
   

   F = ∆P =	1	ρv2A
   	2

   
   

   =	1	× 1.2 × 40 × 40 × 250
   	2

   
   = 2.4 × 10⁵ N (upwards)
   

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9. ​The compressibility of water is 4 × 10^–5 per unit atmospheric pressure. The decrease in volume of 100 cm³ of water under a pressure of 100 atmosphere will be​​​
   

1. 1. 0.4 cm³

   
   
   

   2. 4 × 10^–5 cm³

   
   
   

   3. 0.025 cm³

   
   
   

   4. 0.004 cm³

   
   
   

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1. View Hint View Answer Discuss in Forum

   K =	1	=	(∆V / V)
   	B		P

   
   Here, P = 100 atm, ​
   K = 4 × 10^–5  and V = 100 cm³.
   Hence, ∆V = 0.4 cm³

   Correct Option: A

   K =	1	=	(∆V / V)
   	B		P

   
   Here, P = 100 atm, ​
   K = 4 × 10^–5  and V = 100 cm³.
   Hence, ∆V = 0.4 cm³

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10. In rising from the bottom of a lake, to the top, the temperature of an air bubble remains unchanged, but its diameter gets doubled. If h is the barometric height (expressed in m of mercury of relative density ρ) at the surface of the lake, the depth of the lake is ​
    

1. 1. 8 ρh m

   
   
   

   2. 7ρh m

   
   
   

   3. ​9 ρh m

   
   
   

   4. 12 ρh m

   
   
   

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1. View Hint View Answer Discuss in Forum

   (hρ g + H × l × g) =	4	πr3 = hρ g ×	4	π(2r)3
   	3		3

   
   This gives H = 7hρ
   

   Correct Option: B

   (hρ g + H × l × g) =	4	πr3 = hρ g ×	4	π(2r)3
   	3		3

   
   This gives H = 7hρ
   

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