A hemispherical portion of radius R is removed from the bottom of a cylinder of radius R. The volume of the remaining cylinder is V and mass M. It is suspended by a string in a liquid of density , where it stays vertical. The upper surface of the cylinder is at a depth h below the liquid surface. The force on the bottom of the cylinder by the liquid is
Mg
There is a small hole in a hollow sphere. The water enters in it when it is taken to a depth of 40 cm under water. The surface tension of water is The diameter of hole is :
14mm
The potential energy possessed by a soap bubble, having surface tension equal to 0.04 Nm-1 of diameter 1 cm, is
2× 10-6 J
4× 10-6 J
6× 10-6 J
8× 10-6 J
A glass tube of uniform internal radius (r) has a value separating the two identical ends. Initially, the value is in a tightly closed position. End 1 has a hemispherical soap bubble of radius r. End 2 has sub - hemispherical soap bubbles as shown in figure. Just after opening the valve,
air from end 1 flows towards end 2. No change in the volume of the soap bubbles
air from end 1 flows towards end 2. Volume of the soap bubbles at end 1 decreases
no changes occur
air from end 2 flows towards end 2. Volume of the soap bubble at end 1 increases
A cylinder of height 20 m is completely filled with water. The velocity of efflux of water (in ms-1 ) through a small hole on the side wall of the cylinder near its bottom is
10
20
25.5
5
Spherical balls of radius R are falling in a viscous fluid of viscosity η with a velocity v. The retarding viscous force acting on the spherical ball is
directly proportional to R but inversely proportional to v
directly proportional to both radius R and velocity v
inversely proportional to both radius R and velocity v
inversely proportional to radius R and directly proportional to velocity v.
From the following figures, the correct observation is
the pressure on the bottom of tank A is greater than that at the bottom of B
the pressure on the bottom of the tank A is smaller than that at the bottom of B
the pressure depends on the shape of the container
the pressure on the bottoms of A and B is the same.
If there were no gravity, which of the following will not be there for a fluid ?
Viscosity
Surface tension
Pressure
Archimedes' upward thrust
A closed compartment containing gas is moving with some acceleration in horizontal direction. Neglect effect of gravity. Then the pressure in the compartment is
same everywhere
lower in the front side
lower in the rear side
lower in the upper side
A U-tube of uniform cross-section is partially filled with a liquid I. Another liquid II which does not mix with liquid I is poured into one side. It is found that the liquid levels of the two sides of the tube are the same, while the level of liquid I has risen by 2 cm. If the specific gravity of liquid I is 1.1, the specific gravity of liquid II must be
1.12
1.1
1.05
1.0
