NIMCET 2008 Mathematics PYQ — A rigid body is rotating at the rate of about an axis , where and… | Mathem Solvex | Mathem Solvex
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NIMCET 2008 — Mathematics PYQ
NIMCET | Mathematics | 2008
A rigid body is rotating at the rate of 3 rad/s about an axis AB, where A and B are the points (1,−2,1) and (3,−4,2). The velocity of the point P at (5,−1,−1) of the body is:
Choose the correct answer:
A.
3i+8j+10k
(Correct Answer)
B.
33i+8j+10k
C.
32i−2j+k
D.
4i+j+2k
Correct Answer:
3i+8j+10k
Explanation
Step 1: Find the unit vector along the axis AB
The direction of the axis is given by the vector AB:
AB=(3−1)i^+(−4−(−2))j^+(2−1)k^
AB=2i^−2j^+k^
The magnitude of AB is:
∣AB∣=22+(−2)2+12=4+4+1=3
The unit vector n^ along the axis is:
n^=∣AB∣AB=32i^−2j^+k^
Step 2: Find the angular velocity vector ω
The magnitude of angular velocity ω is 3 rad/s.
ω=ωn^=3(32i^−2j^+k^)=2i^−2j^+k^
Step 3: Find the position vector r
We can take point A(1,−2,1) as the reference point on the axis. The vector r from A to P(5,−1,−1) is:
