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UPSC Civil Service Exam Questions - Engineering

Q1:

A velocity field with no components in the y and z directions is given by V = 6 + 2xy +t2
The acceleration along the x-direction at a point (3, 1, 2), at time 2, is

A 8 units

B 16 units

C 28 units

D 36 units

ANS:D - 36 units

V= (6+2xy+t2) i

Acceleration at x axis = (udu/dx) + (du/dt)------>(a)
(6+ 2xy+t2)= u ------------->(1)
du/dx= 2y ------------------>(2)
du/dt= 2t ------------------->(3)

Put 1,2,3 in equation (a).
(6+2xy+t2)*2y+(2t)---------->(b)
Points given ( 3,1,2) at time =2Subsitute points and time in equation (b).
Ans 36 units.