Gravitation question bank (Physics)

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 $\left(\mathrm{c}\mathrm{o}\mathrm{s}{0}^o=1\right)$

If the density of the earth is doubled keeping radius constant, find the new acceleration due to gravity? $\left(g=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)$