Page 26 - CITS - WCS - Mechanical

WORKSHOP CALCULATION - CITS

Mass, Weight, Volume, Density, Viscosity, Specific gravity and related problems

Density is explains as the mass of an object per unit volume, whereas relative density, also known as specific
gravity, which is defined as the ratio of a substance’s weight to the weight of the same volume of water. Density
& specific gravity are two different concepts. SI Unit is kg/m3
W = mg
To calculate the weight, use the following general formula: W=mg. Here, “W” is the weight of the object, “m” is the
mass of the object, and “g” is the acceleration due to gravity. On Earth, the value of g is 9.8 m / s .
2
Viscosity: Viscosity is a measure of a fluid’s resistance to flow. The SI unit of viscosity is Poiseiulle (PI). Its
other units are newton-second per square metre (N s m- ) or Pascal-second (Pa s.) The dimensional formula of
2
viscosity is [ML T ].A fluid with large viscosity resists motion due to its molecular makeup gives it a lot of internal
-1 -1
friction. A fluid with low viscosity flows easily for the reason that, its molecular makeup results in very little friction
when it is in motion.
Examples
Q. If the area of a triangle with base ‘x’ is equal to the area of a square with side x. then the altitude of the
triangle is:
a) x/2 b) x c) 2x d) 3x e) None of these
Let, altitude of the triangle is – haIf base ‘x’, then the area of the triangle is – ½ (x × h) square units, if side ‘x’, then
the area of the square is – square units
Now, as per the given condition, ½ (x × h) =x²or, h = 2x (Answer)
So, option (c) is correct.

Q. Find the area of a triangle whose sides are 5 , 5 & 6 cm
a) 12 cm² b) b) 14 cm² c) 16 cm² d) 10 cm² e) None of these 5 5
So, area of the triangle = ½ (6 ×4) 1 H
A= 6x4
= 12cm² (Answer) 2 5
2
So, option (a) is correct. H = 5 -3 2
= 4
Q. A cone and a hemisphere have equal bases and equal heights. Find out the ratio of their curved
surface area.

a) 1: √2 b) √2:1 c) 2:1 d) 1:2 e) None of these
→Let the base radius of hemisphere = r unit.
Base radius of cone = r unit.
Height of cone = base radius of hemisphere = r unit

So, Slant height of cone (l) =√(h²+r²)=√(r²+r²)=√2r unit
The ratio between the curved surface area of hemisphere and cone is –
= 2πr² :πrl = 2π²r: πr (√2r)=2 :√2= √2 : 1 ( Answer)
So, option (b) is correct.

Q. A rectangular piece of paper 11 cm × 4 cm is folded without overlapping to make a cylinder of height 4
cm. Find the volume of the cylinder.
Solution: Length of the paper will be the perimeter of the base of the cylinder and width will be its height.

Circumference of base of cylinder = 2πr = 11 cm
2 x 22/7 x r = 11 cm
r = 7/4 cm
Volume of cylinder = πr h = (22/7) x (7/4) x 4
2
2
= 38.5 cm 3

13

CITS : WCS - Mechanical - Exercise 5 CITS : WCS - Mechanical - Exercise 5