Two spherical objects differ in size and mass. Object A has a mass that is eight

Question

Two spherical objects differ in size and mass. Object A has a mass that is eight times the mass of object B. The radius of object A is twice the radius of object B. How do their densities compare?
a) ?A > ?B
b) ?A < ?B
c) ?A = ?B
d) Not enough information is given to compare their densities.

A horizontal pipe narrows from a diameter of 10 cm at location A to 5.0 cm at location B. For a nonviscous incompressible fluid flowing without turbulence from location A to location B, how does the flow speeds v (in m/s) compare at the two locations?
a) vA = vB
b) vA = 1/2vB
c) vA = 1/4vB
d) vA = 2vB
e) vA = 4vB

Explanation / Answer

1) The density of the sphere is = m/V = m/[4/3 R3] R is the radius of the sphere = 3m/4R3 Given mA = 8mB and RA = 2RB A = 3mA /4RA3 B = 3mB /4RB3 A = 3(8mB) /4(2RB)3 A = 3mB /4RB3 A = B OPtion C is correct 2) Equation of continuty states Av = constant A is the area of cross section v is the speed of the fluid Given RA = 2RB RA2vA = RB2vB (2RB)2vA = RB2vB 4vA = vB vA = 1/4 vB Option c is correct Option c is correct

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