1. The approximate depth of an ocean is 2700 m. The compressibility of water is 45.4 × 10^–11 Pa^–1 and density of water is 10³ kg/m³.What fractional compression of water will be obtained at the bottom of the ocean ?​
   

1. 1. 1.0 × 10^–2

   
   
   

   2. 1.2 × 10^–2

   
   
   

   3. ​1.4 × 10^–2

   
   
   

   4. 0.8 × 10^–2

   
   
   

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1. View Hint View Answer Discuss in Forum

   Compressibility of water, ​K = 45.4 × 10^–11 Pa^–1
   density of water P = 10³ kg/m³ ​
   depth of ocean, h = 2700 m
   ​

   We have to find	∆V	= ?
   	V

   
   As we know, compressibility,
   

   =	1	=	(∆V / V)	(P = ρ g h)
   	B		P

   
   So , (∆V / V) = K ρ g h
   = 45.4 × 10^–11 × 10³ × 10 × 2700  = 1.2258 × 10^–2

   Correct Option: B

   Compressibility of water, ​K = 45.4 × 10^–11 Pa^–1
   density of water P = 10³ kg/m³ ​
   depth of ocean, h = 2700 m
   ​

   We have to find	∆V	= ?
   	V

   
   As we know, compressibility,
   

   =	1	=	(∆V / V)	(P = ρ g h)
   	B		P

   
   So , (∆V / V) = K ρ g h
   = 45.4 × 10^–11 × 10³ × 10 × 2700  = 1.2258 × 10^–2

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2. 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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3. ​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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4. 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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5. 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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