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# Objects at rest on earth's surface move in circular paths with a period of 24 hours. What should be the length of the day so that such objects experience weightlessness, so that they are in "true orbit"

$(a)\;2.5\;hrs \quad (b)\;1.4\;hrs \quad (c)\; 12\;hrs \quad (d)\;6.2\;hrs$

$W=m(g-Rw^2)=0$
ie $w=\sqrt {(g/R)}$ so that
$T=\large\frac{2 \pi}{w}$
$\quad=2 \pi \sqrt {\large\frac{R}{g}}$
$\quad=2 \pi \sqrt {\large\frac{6400 \times 10^3}{10}}$
$\quad=5028.5 \;seconds$
$\quad=1.4 \;hrs$
Hence b is the correct answer.