Pressure in Fluids — Pascal's law, hydraulic press

Q47.Two soap bubbles of radius 2 cm and 4 cm , respectively, are in contact with each other. The radius of curvature of the common surface, in cm , is ______ . and

Q27.A small rigid spherical ball of mass M is dropped in a long vertical tube containing glycerine. The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball, then the viscous force acting on the ball will be (consider g as acceleration due to gravity) (1) 2 Mg (2) Mg (3) 3 2 Mg (4) Mg2

Q41. A tube of length L is shown in the figure. The radius of cross section at the point (1) is 2 cm and at the point (2) is 1 cm , respectively. If the velocity of water entering at point (1) is 2 m/s, then velocity of water leaving the point (2) will be (1) 4 m/s (2) 2 m/s (3) 6 m/s (4) 8 m/s

Q30.A massless spring gets elongated by amount x1 under a tension of 5 N . Its elongation is x2 under the tension of 7 N . For the elongation of (5x1 −2x2), the tension in the spring will be, (1) 39 N (2) 15 N (3) 11 N (4) 20 N

Q32.Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is P1 . The reading of the pressure gauge falls to P2 when the valve is opened. The speed of water flowing in the pipe is proportional to (1) P1 −P2 (2) (P1 −P2)4 (3) (P1 −P2)2 (4) √P1 −P2

Q48.An air bubble of radius 1.0 mm is observed at a depth of 20 cm below the free surface of a liquid having surface tension 0.095 J/m2 and density 103 kg/m3 . The difference between pressure inside the bubble and atmospheric pressure is _____ N/m2 . (Take g = 10 m/s2 )