Two small aluminum and brass spheres of equal radii released to a tall (large) cylinder containing a viscous liquid.Consider the following statements..(A) The initial accelerations of both the spheres are same.(B) Both spheres obtain terminal velocities at the same instant.(C)Terminal velocities of two spheres are equal.

The statements can be analyzed as follows:

(A) The initial accelerations of both the spheres are the same. This statement is true. When the spheres are released, they both experience the same acceleration due to gravity initially. The only forces acting on them are gravity (downwards) and the buoyant force (upwards). Since both spheres have the same volume, the buoyant force is the same for both. Therefore, their initial accelerations are the same.

(B) Both spheres obtain terminal velocities at the same instant. This statement is false. Terminal velocity is reached when the force due to gravity is balanced by the drag force from the liquid. The drag force depends on the shape, size, and velocity of the object, as well as the properties of the fluid. Since aluminum and brass have different densities, they will experience different drag forces and will reach terminal velocity at different times.

(C) Terminal velocities of two spheres are equal. This statement is also false. Terminal velocity depends on the balance between the force of gravity and the drag force. Since the spheres are made of different materials (aluminum and brass), they have different densities. This means they will have different weights when submerged in the liquid, leading to different terminal velocities.