Question

The angular velocity of earth at present is $ω$ With what angular velocity should it rotate $ω$ that weight of a body at the equator appears $ω$ be zero?

• A. 289 $ω$
• B. 17 $ω$
• C. 8 $ω$
• D. 2 $ω$

Answer 1

Answer: (B)

The body will appear weightless only when the centripetal force equals the weight of the body.
$∴\frac{m{v}^2}{R}=mg$
Since, $v=Rω$
$\frac{m(Rω{)}^2}{R}=mg$
$⇒mR{ω}^2=mg$
$⇒ω=\sqrt{\frac{g}{R}}$
Standard value $(ω)$ at present is
$ω=\frac{2π}{T}=\frac{2π}{86400}rad{s}^{−1}$
$=7.3×10^{−5}rad{s}^{−1}$
and ${ω}^{′}=\sqrt{\frac{g}{R}}$
$=\sqrt{\frac{9.8}{6.4×10^6}}=1.2×10^{−3}$
$∴{ω}^{′}≈17ω$.