Consider a particle of mass $m$ suspended by a string at the equator. Let $R$ and $M$ denote radius and mass of the earth. If $\omega$ is the angular velocity of rotation of the earth about its own axis, then the tension on the string will be $\left(\cos 0^{\circ}=1\right)$

Six very long insulated copper wires are bound together to form a cable. The currents carried by the wires are $I_1=+10 \mathrm{~A}, I_2=-13 \mathrm{~A}, I_3=+10$ $\mathrm{A}, I_4=+7 \mathrm{~A}, I_5=-12 \mathrm{~A}$ and $I_6=+18 \mathrm{~A}$. The magnetic induction at a perpendicular distance of 10 cm from the cable is $\left(\mu_0=4 \pi \times 10^{-7} \mathrm{~Wb} / \mathrm{A}-\mathrm{m}\right)$

The fundamental frequency of sonometer wire increases by 9 Hz , if its tension is increased by $69 \%$, keeping the length constant. The frequency of the wire is