Last Activity: 15 Years ago
Density D = mass/Volume
or, D = m/l3
Take log of both sides.
log(D) = log(m) - 3 log(l)
Now, differentiate both sides.
Differential of log(x) is 1/x dx.
x can be anything.
So, here, we have
(1/D) dD =(1/m) dm - 3 (1/l) dl [Because log(1/2) is a constant, and
derivative of any constant is zero]
Now, dK is nothing but delta(K).
So, dK is the error in measurement of K.
dK/K is the relative error in measurement of K.
Percentage error is relative error x 100
Hence,
dK/K = dm/m + 3 dl/l [Note that the minus sign changes to plus, because errors always add up, unlike derivatives]
We are given that dm/m = 0.1% = 0.001
Also, dl/l = 0.3% = 0.003
Therefore, Relative error in measurement of K = dK/K = 0.001 + 3(0.003) = 0.001 + 0.009 = 0.01
Percentage error = 0.01 x 100 = 1 %
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Get your questions answered by the expert for free
Last Activity: 2 Years ago
Last Activity: 2 Years ago
Last Activity: 2 Years ago
Last Activity: 2 Years ago
Last Activity: 2 Years ago