Question

A) Ball made of wood and ball made of aluminum, of the same radius are placed into reservoir with water. Aluminum ball after sinking rests at the bottom, wooden ball floats. Which ball experiences greater buoyancy force?

a

Aluminum

b

Wooden

c	Buoyncy forces are the same

d	There is not enough information

B) Water flows through a pipe with speed of 18 m/s. Pipe suddenly widens to 3 times of its initial diameter. The speed of water in broader part of a pipe is:

a

2 m/s

b

6 m/s

c

18 m/s

d

54 m/s

Answer 1

answer (A) It is quite tricky question since here its not given that the wooden ball is floating partially or is how much is it submerged in water. The buayant force is equal to the wieight of water displaced by the balls. Since the both the balls are of equal volume so both will displace equal weights of water, but not in this case because, the aluminium ball is completely submrged in water so it will displace water equal to its total volume but the wooden ball is not completely submerged in water so it will displace lesser water than the aluminium ball.

Hence the buoyant force on the wooden ball is lesser than the buoyant force on aluminium ball.

Answer (B). According to equation of continuity A1V1= A2V2. Where A1 & A2 are cross section areas of pipe in which fluid is flowing and V1, V2 are the velocities of the fluid flow at the respective cross sections.

Here final cross setion area is 3 times the initial one. So A1= A and A2= 3A, given V1= 18m/s and V2=?.

So A*18=3A*V2

=> V2=18/3=6 m/s. The fluid speed becomes 6 m/s when pipe widens up 3 times its initial value.