Question

A physical quantity y = a⁴b²/(cd⁴)⅓ has for observable a,b,c,and d. the percentage error in a,b,c, and d are 2%, 3%, 4%, and 5% respectively. find the error in y​

Answer 1

Answer:

Given →

physical quantity y=

(c⋅d

4

)

1/3

a

4

⋅b

2

Percentage error in a=2%,b=3%,c=40%

d=5%

Percuntage error in y=?

Calculating error with differentiation method

Physical qty y=

(c⋅d

4

)

1/3

a

4

⋅b

2

Rewriting y=

c

1/3

⋅d

4/3

a

4

⋅b

2

On Taking logarithm both sides we get-

logy=4⋅loga+2logb−

3

1

logc−

3

4

logd

for maximum permissible error in y rewrite as

y

dy

=4⋅

a

da

+

b

2⋅db

+

3

1

⋅

c

dc

+

3

4

⋅

d

d(d)

Now

a

da

=2%

b

db

=3%

c

dc

=4%

d

d(d)

=5% (given)

So we get

y

dy

y

dy

=4⋅(2%)+2(3%)+

3

1

⋅(4%)+

3

4

⋅(5%)

=22%