A physical quantity z depends on a,b,c,d as z = a²b²ᐟ³/(√c·d³). The percentage errors in a,b,c,d are 2%, 1.5%, 4% and 2.5%, respectively. Find the percentage error in z.
Physics · Unit dimension and error
JEE Mains 2020

Question

A physical quantity z depends on a,b,c,d as z = a²b²ᐟ³/(√c·d³). The percentage errors in a,b,c,d are 2%, 1.5%, 4% and 2.5%, respectively. Find the percentage error in z.

G1 Physics · Accepted Answer

For z=a²b²ᐟ³/(c¹ᐟ²d³), maximum percentage error =2(2)+(2/3)(1.5)+(1/2)(4)+3(2.5)=14.5%. Correct answer: B.