Question

5. A physical quantity P is described by the relation P=a? b c d. It the relative errors in the
measurement of a, b, c and d respectively, are 2%, 1%, 3% and 5%, then the relative error in P will be
[JEE Main 17]
(A) 25%
(B) 12%
(C) 8%
(D) 32%​

Answer 1

ANSWER

P=a

1/2

.b

2

.c

3

.d

−4

Taking log on both sides

logP=

2

1

loga+2logb+3logc−4logd

Now differentiating on both sides

P

dP

=

2a

da

+2

b

db

+3

c

dc

−4

d

d(d)

or

P

ΔP

=

2a

Δa

±2

b

Δb

±3

c

Δc

±4

d

Δd

Now, given,

a

Δa

×100=2,

⇒

b

Δb

×100=1,

⇒

c

Δc

×100=3,

⇒

d

Δd

×100=5,

⇒

P

ΔP

×100=

2

2

±2×1±3×3±4×5

⇒

P

ΔP

×100=32%

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