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physics

mechanics

Easy

Question

A force of $left parenthesis 2 i with hat on top minus 4 j with hat on top plus 2 k with hat on top right parenthesis$ Newton acts at a point $left parenthesis 3 i with hat on top plus 2 j with hat on top minus 4 k with hat on top right parenthesis$ metre from the origin. The magnitude of torque is -

2.444 N-m
zero
24.4 N-m
0.244 N-m

The correct answer is: 24.4 N-m

$F with rightwards arrow on top equals left parenthesis 2 i with hat on top minus 4 j with hat on top plus 2 k with hat on top space right parenthesis r with rightwards arrow on top equals left parenthesis 3 i with hat on top plus 2 j with hat on top minus 4 k with hat on top space right parenthesis T o r q u e space equals space r with rightwards arrow on top cross times F with rightwards arrow on top$
$vertical line left parenthesis 3 i with not stretchy hat on top plus 2 j with not stretchy hat on top minus 4 k with not stretchy hat on top right parenthesis cross times left parenthesis 2 i with not stretchy hat on top minus 4 j with not stretchy hat on top plus 2 k with not stretchy hat on top right parenthesis vertical line$
$open vertical bar table row i j k row 3 2 cell negative 4 end cell row 2 cell negative 4 end cell 2 end table close vertical bar$
$i with not stretchy hat on top left parenthesis 4 minus 16 right parenthesis minus j with not stretchy hat on top left parenthesis 6 plus 8 right parenthesis plus k with not stretchy hat on top left parenthesis negative 12 minus 4 right parenthesis$
$equals vertical line minus 12 i with not stretchy hat on top minus 14 j with not stretchy hat on top minus 16 k with not stretchy hat on top vertical line$
$equals square root of left parenthesis 12 right parenthesis squared plus left parenthesis 14 right parenthesis squared plus left parenthesis negative 16 right parenthesis squared end root equals 24.4 N minus m$

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