Three balls are in water. ball 1 floats, with half of it exposed above the water level. ball 2, with a density less than the density of water is held below the surface by a cord anchored to the bottom of the container, so that it is fully submerged. ball 3, of same radius as ball 2, but of greater mass, is suspended from a rope so that it is fully submerged. part (a) which is true for ball 1? choose the best answer. a. the magnitude of the buoyancy force is less than that of the ball's weight. b. the magnitude of the buoyancy force is equal to that of the ball's weight. c. the magnitude of the buoyancy force is more than that of the ball's weight. d. the magnitude of the buoyancy force is exactly one half of that of the ball's weight. part (b) which is true for ball 2? choose the best answer. a. the magnitude of the buoyancy force is less than that of the ball's weight. b. the magnitude of the buoyancy force is larger than that of the ball's weight. c. the magnitude of the buoyancy force is equal to that of the ball's weight. d. the magnitude of the buoyancy force is exactly one half of that of the ball's weight. part (c) consider ball 2 and ball 3. which one experiences the larger buoyancy force? choose the best answer a. ball 2 b. they both have the same buoyancy force. c. the answer depends on the forces in the ropes. d. ball 3

(a) The magnitude of the buoyancy force is equal to that of the ball's weight. Hence, option (B) is correct.

(b) The magnitude of the buoyancy force is equal to that of the ball's weight. Hence, option (B) is correct.

(c) Both ball 2 and ball 3 will experience same amount of buoyant force from water. Hence, option (c) is correct.

(a)

The buoyant force (B) by water is in equilibrium with the force (F) exerted by ball and weight of ball (W).

Since ball 1 is floating, then net vertical force (F) acting on the ball 1 is zero. Which means, F = 0. Then above expression is,

Thus, we can conclude that the magnitude of the buoyancy force is equal to that of the ball's weight. Hence, option (B) is correct.

(b)

Since ball 2 is fully submerged. Then, the net vertical force will cause a tension on the ball (T). Then, the buoyant force acting on ball 2 is given as,

Thus, we can conclude that the magnitude of the buoyancy force is larger than that of weight of ball 2. Hence, option (b) is correct.

(c)

The concept of Buoyancy says that, "The buoyant force acting on the ball is equal to the weight of water displaced by the ball." And the weight of ball is directly proportional to the volume of ball. Both ball 2 and ball 3 have same volume, so they have same weight, hence they will also experience same magnitude of buoyant force.

Thus, we can conclude that both ball 2 and ball 3 will experience same amount of buoyant force from water. Hence, option (c) is correct.

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(a) Option B

The magnitude of the buoyancy force is equal to that of the ball's weight.

(b) Option B

The magnitude of the buoyancy force is larger than that of the ball's weight.

(c) Option B

They both have the same buoyancy force.

Explanation:

(a)

Ball 1

The sum of vertical forces is zero hence therefore

B-mg=0 where B is buoyancy force, m is mass of ball, g is acceleration due to gravity

B=mg  

mg is weight of ball  

Therefore, option B, The magnitude of the buoyancy force is equal to that of the ball's weight

(b)

Ball 2

The sum of vertical forces is zero hence therefore

B-T-mg=0 where B is buoyancy force, m is mass of ball, g is acceleration due to gravity and T is tension in the string

B=mg+T

Therefore, option B, The magnitude of the buoyancy force is larger than that of the ball's weight.

(c )

Ball 2 and 3

They have similar buoyancy force since the weight displaced by the body equals the buoyancy force. In this case, the weight of the displaced fluid is proportional to the volume of the ball since the two balls have same volume. It therefore means that their buoyancy forces are also the same.

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .