The equation of the circle passing through the points (1, 0) and (0,1) and having the smallest radius is:

If a circle passes through the point (a, b) and cuts the circle orthogonally, then the equation of the locus of its centre is‐

Hence locus of the given condition is optionD

The square of the length of tangent from (3, -4) on the circle

Hence option C is correct

A hollow sphere of mass M and radius r is immersed in a tank of water (density r_w). The sphere would float if it were set free. The sphere is tied to the bottom of the tank by two wires which makes angle 45° with the horizontal as shown in the figure. The tension T₁ in the wire is :

A small wooden ball of density r is immersed in water of density to depth h and then released. The height H above the surface of water up to which the ball will jump out of water is

A dumbbell is placed in water of density r. It is observed that by attaching a mass m to the rod, the dumbbell floats with the rod horizontal on the surface of water and each sphere exactly half submerged as shown in the figure. The volume of the mass m is negligible. The value of length l is

A slender homogeneous rod of length 2L floats partly immersed in water, being supported by a string fastened to one of its ends, as shown. The specific gravity of the rod is 0.75. The length of rod that extends out of water is :

Two cubes of size 1.0 m sides, one of relative density 0.60 and another of relative density = 1.15 are connected by weightless wire and placed in a large tank of water. Under equilibrium the lighter cube will project above the water surface to a height of

An open-ended U-tube of uniform cross-sectional area contains water (density 1.0 gram/centimeter³) standing initially 20 centimeters from the bottom in each arm. An immiscible liquid of density 4.0 grams/ centimeter³ is added to one arm until a layer 5 centimeters high forms, as shown in the figure above. What is the ratio h₂/h₁ of the heights of the liquid in the two arms?

A light semi cylindrical gate of radius R is piovted at its mid point O, of the diameter as shown in the figure holding liquid of density r. The force F required to prevent the rotation of the gate is equal to

In the figure shown, the heavy cylinder (radius R) resting on a smooth surface separates two liquids of densities 2r and 3r. The height ‘h’ for the equilibrium of cylinder must be

A liquid of mass 1 kg is filled in a flask as shown in figure. The force exerted by the flask on the liquid is (g = 10 m/s²)[Neglect atmospheric pressure]:

An open cubical tank was initially fully filled with water. When the tank was accelerated on a horizontal plane along one of its side it was found that one third of volume of water spilled out. The acceleration was

Figure shows a three arm tube in which a liquid is filled upto levels of height l. It is now rotated at an angular frequency w about an axis passing through arm B. The angular frequency w at which level of liquid in arm B becomes zero.

A fluid container is containing a liquid of density r is accelerating upward with acceleration a along the inclined place of inclination a as shown. Then the angle of inclination q of free surface is :

The area of cross-section of the wider tube shown in figure is 800 cm² If a mass of 12 kg is placed on the massless piston, the difference in heights h in the level of water in the two tubes is :