Question

Given the kinetic energy of body is T = ^1⁄2 mv^2. If the mass of body changes from 100 kg to 100 kg and 500 gm and velocity of a body changes from 1600 mt/sec to 1590 mt/sec. Then find the approximate change in T.

(a) 960000 J decrease in value

(b) 960000 J increase in value

(c) 450000 J decrease in value

(d) 450000 J increase in value

This question was addressed to me in an internship interview.

This question is from Errors and Approximations in section Partial Differentiation of Engineering Mathematics

Answer 1

Right answer is (a) 960000 J decrease in value

To elaborate: Given T = ^1⁄2 mv^2

Now taking log and differentiating,

δT = 0.5[v^2 δm + 2mvδv]

Now, v = 1600 mt/sec, m = 100kg, δv = -10,         δm = 0.5

Then,

δT = -960000 J => decrese in value of T by 960000 J.