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Question

Moment of the force, F=(4^i+5^j6^k) N acting at point P(2,0,3) m about the point Q(2,2,2) m is given by :

A
(7^i8^j4^k) N.m
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B
(4^i^j8^k) N.m
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C
(8^i4^j7^k) N.m
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D
(7^i4^j8^k) N.m
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Solution

The correct option is D (7^i4^j8^k) N.m
Moment of the force F is given as,
τ=r×F ...(i)


F=4^i+5^j6^k
Position vector(r) of P with respect to reference point Q is,
r=(2^i+0^j3^k)(2^i2^j2^k)
r=0^i+2^j1^k
Substituting in Eq (i),
τ=r×F=∣ ∣ ∣^i^j^k021456∣ ∣ ∣
τ=^i(12(5))^j(0(4))+^k(08)
τ=7^i4^j8^k
The moment of the force F about point Q at point P is :
(7^i4^j8^k) N.m

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