Question

A pendulum having a bob of mass m is hanging in a ship sailing along the equator form east to west. When the strip is stationary with respect to water, the tension in the string is $T_0$. The difference between $T_0$ and earth attraction on the bob, is

• A. $\frac{mg+m{\omega }^{2}R}{2}$
• B. $\frac{m{\omega }^{2}R}{3}$
• C. $\frac{m{\omega }^{2}R}{2}$
• D. $m{\omega }^{2}R$

Answer 1

The correct option is D $m{\omega }^{2}R$

The attraction of earth on the bob $=$ Weight of bob $=mg$

Also due to the rotation of earth, a centripetal force acts on the bob $=m{\omega }^{2}R$ towards earth

Hence, total tension in string balancing the weight of bob $=T_0=mg+m{\omega }^{2}R$

Hence, difference between tension and earth's attraction on bob $=T_0-mg=m{\omega }^{2}R$