Physics Pressure in Fluids and Atmospheric Pressure Numerical4a
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Q1 A hammer exerts a force of 1.5N on each of the two nails A and B. The area of cross section of tip of nail A is 2mm2 while that of nail B is 6 mm2 . Calculate pressure on each nail in pascal.
Solution :
Q2 A block of iron of mass 7.5kg and of dimensions 12cm x 8cm x 10cm is kept on a table top on its base of side 12cm x 8cm. Calculate : (a) thrust and (b) pressure exerted on the table top. Take 1kgf = 10N.
Solution :
Q3 A vessel contains water up to a height of 1.5m. Taking the density of water 103 kg m-3 , acceleration due to gravity 9.8ms-2 and area of base vessel 100cm2 , calculate: (a) the pressure and (b) the thrust, at the base of vessel.
Solution :
Q4 The area of base of a cylindrical vessel is 300cm2 . Water (Density = 1000 kg m-3 ) is poured into it up to a depth of 6cm. Calculate: (a) the pressure and (b) the thrust of water on the base. (g = 10m/s2 ).
Solution :
Q5 (a) Calculate the height of a water column which will exert on its base the same pressure as the 70cm column of mercury. Density of mercury is 13.6 g cm-3 .
(b) Will the height of the water column in part (a) change if the cross section of the water column is made wider? .
Solution :
Q6 The pressure of water on the ground floor is 40,000 Pa and on the first floor is 10,000Pa. Find the height of the first floor. (Take: density of water = 1000kg m-3 , g=10m/s2 )
Solution :
Q7 A simple U tube contains mercury to the same level in both of its arms. If water is poured to a height of 13.6cm in one arm, how much will be the rise in mercury level in the other arm? Given: density of mercury = 13.6 x 103 kg m-3 and density of water = 103 kg m-3
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Q8 In a hydraulic machine, a force of 2N is applied on the piston of area of cross section 10cm2 . What force is obtained on its piston of area of cross section 100cm2?
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Q9 What should be the ratio of area of cross section of the master cylinder and wheel cylinder of a hydraulic brake so that a force of 15N can be obtained at each of its brake show by exerting a force of 0.5N on the pedal?
Solution :
Q10 The areas of pistons in a hydraulic machine are 5cm2 and 625 cm2 . What force on the smaller piston will support a load of 1250N on the larger piston? State any assumption which you make in your calculation. Assumption: There is no friction and no leakage of liquid.
Solution :
Q11 (a) The diameter of neck and bottom of a bottle are 2cm and 10cm respectively. The bottle is completely filled with oil. If the cork in the neck is pressed in with a force of 1.2kgf, what force is exerted on the bottom of the bottle?
(b) Name the law/principle you have used to find the force in part (a)
Solution :
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Q12 A force of 50kgf is applied to the smaller piston of a hydraulic machine. Neglecting friction, find the force exerted on the large piston, if the diameters of the pistons are 5cm and 25cm respectively.
Solution :
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Q13 Two cylindrical vessels fitted with pistons A and B of area of cross section 8cm2 and 320cm2 respectively, are joined at their bottom by a tube and they are completely filled with water. When a mass of 4kg is placed on piston A, find: (i) the pressure on piston A, (ii) the pressure on piston B, and (iii) the thrust on piston B
Solution :
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Q14 What force is applied on a piston of area of cross section 2cm2 to obtain a force 150N on the piston of area of cross section 12cm2 in a hydraulic machine?
Solution :
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