1. Which of the following is not a unit of density?
a) Kg/m3
b) N/m3
c) N.s2/m4
d) g/cm3
Explanation: Dimensions of density are M1L-3, which is not the dimension of N/m3, so N/m3 is not the unit of density.
2. What is the density of a substance of mass 10 grams and volume 5 liters?
a) 2 kg/m3
b) 20 kg/m3
c) 200 kg/m3
d) 2000 kg/m3
Explanation: Density = (10*10-3)/(5*10-3) = 2 kg/m3.
3. A solid of density d is dropped in a liquid of density D, if d>D then,
a) Solid will completely sink
b) Solid will completely float
c) Solid will partially sink
d) None of the mentioned
Explanation: Since the density of solid is greater than that of liquid, this means that the weight of the solid will be higher than its buoyancy force so it will completely sink.
4. A liquid of mass 10 kg is enclosed in a cylinder of radius 1 m and length 5 m, what is the density of liquid?
a) 0.54 kg/m3
b) 0.44 kg/m3
c) 0.63 kg/m3
d) 0.83 kg/m3
Explanation: Volume of cylinder = π(12)5 = 5π m3, => Density = 10/5π = 0.63 kg/m3.
5. What is the density of a liquid of mass 20 kg, enclosed in a cuboid of surface areas of three sides as 1 m2, 2 m2, 5 m2, and one of its sides is 2 m?
a) 1 kg/m3
b) 2 kg/m3
c) 3 kg/m3
d) 4 kg/m3
Explanation: Sides of the cuboid are 1m, 2m and 5m, => volume = 10 m3, density = 20/10 = 2 kg/m3.
6. What is the density of a liquid of mass 10 kg and contained in a cylinder of radius 5 m and surface area (excluding top and bottom) of 10π m2?
a) 0.2π kg/m3
b) 0.4π kg/m3
c) 0.5π kg/m3
d) 0.6π kg/m3
Explanation: Height of cylinder = 10π/(2π*5) = 1 m, => volume of cylinder = π(52)1 = 25π, => density of liquid = 10/25π = 0.4π kg/m3.
7. What is the mass of a liquid having density 20 kg/m3, enclosed in a sphere of radius 1 m?
a) 80.7 kg
b) 83.7 kg
c) 85.7 kg
d) 88.7 kg
Explanation: Volume of liquid = (4/3)π13 = 4.18 m3, => mass of liquid = 20*4.18 = 83.7 kg.
8. What is the mass of a cube having surface area 24 m2, and density 1 kg/m3?
a) 1
b) 2
c) 4
d) 8
Explanation: Side of the cube = (24/6)0.5 = 2 m, => mass of cube = 1*23 = 8 kg.
9. An empty vessel has with mass 5 kg with volume 0.1 m3, is now completely filled with a liquid of density 100 kg/m3, what is the final density of the cylinder?
a) 50 kg/m3
b) 100 kg/m3
c) 150 kg/m3
d) 200 kg/m3
Explanation: Mass of liquid = 100*0.1 = 10 kg, => total mass of cylinder = 10 + 5 = 15 kg, => final density of liquid = 15/0.1 = 150 kg/m3.
10. A cylinder completely filled with water has density = 10 kg/m3 and volume 5 m3 , now a cube with side 1 m and density 25 kg/m3 is dipped into the cylinder with some water dropping out, what is the final density of cylinder?(neglect the mass of cylinder)
a) 13 kg/m3
b) 15 kg/m3
c) 17 kg/m3
d) 19 kg/m3
Explanation: Initial mass of cylinder = 10*5 = 50 kg, mass of cube = 25*1 = 25 kg, => mass of water coming out = 10*1 = 10 kg, => final density of cylinder = (50 + 25 – 10)/5 = 13 kg/m3.