Answer:
Explanation:
The accuracy of metre rule is ±0.5mm
Therefore the length becomes 12±0.5mm
The accuracy of micrometers is ±0.01mm
Then the width is 5.98±0.01mm
a. Area of rectangle = Length × breadth.
Area=12±0.5mm ×5.98±0.01mm
For area calculation
A= l×b
A=12×5.98
A=71.76mm2
For error of multiplication
A=l × b
∆A/A= ∆l/l+ ∆b/b
∆A=A(∆l/l +∆b/b)
∆A=71.76(0.5/12+0.01/5.98)
∆A=3.11mm2
Therefore A= 71.76±3.11mm2
b. Ratio of width to length
U=w/l
U=5.98±0.01mm/12±0.5mm
U=w/l = 5.98/12=0.498
Error calculation
Same rule is applied to both multiplication and division
∆U/U= ∆w/w+ ∆l/l
∆U= U(∆w/w+ ∆l/l)
∆U=0.498(0.01/5.98+0.5/12)
∆U=0.02
Therefore
U=0.5±0.02
c. Perimeter of the rectangle is given by
P=2(l+w)
l=12±0.5mm
w=5.98±0.01mm
P=2(12+5.98)
P=35.96mm
Error calculation for addition and multiplication of a constant
∆P=2( ∆l+∆w)
∆P=2(0.01+0.5)
∆P=1.02mm
Therefore
Perimeter = 35.96±1.02mm
d. Difference between length and width
U=l-w
l=12±0.5mm
w=5.98±0.01mm
U= 12-5.98
U=6.02mm
Error is the same method with questions c
∆U=∆l+∆w
∆U=0.5+0.01
∆U=0.51mm
Therefore,
U=6.02±0.51mm
e. The ratio length to width
U=l/w
U=12±0.01mm/5.98±0.5mm
U=w/l = 12/5.98=2.01
Error calculation
Same rule is applied to both multiplication and division
∆U/U= ∆w/w+ ∆l/l
∆U= U(∆w/w+ ∆l/l)
∆U=2.01(0.01/5.98+0.5/12)
∆U=0.09
Therefore
U=2.01±0.09
U=2±0.1 approximately
