Question

A physical quantity P is described by the relation p = a^1/2 b² c³ d^-4. If 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 ______.

Options

• 8%

• 12%

• 32%

• 25%

Answer 1

A physical quantity P is described by the relation p = a^1/2 b² c³ d^-4. If 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 32%.

Explanation:

Given, P = a^1/2 b² c² d^-4

Maximum relative error,

`(Delta"P")/"P"=1/2(Delta"a")/"a"+2(Delta"b")/"b"+3(Delta"c")/"c"+4(Delta"d")/"d"`

= `1/2xx2+2xx1+3xx3+4xx5`

= 32%