A bead of mass m stays at point P(a, b) on a wire bent in the shape of a parabola y = 4Cx² and rotating with angular speed $$\omega $$ (see figure). The value of $$\omega $$ is (neglect friction) :

Magnetic materials used for making permanent magnets (P) and magnets in a transformer (T) have different properties of the following, which property best matches for the type of magnet required?

The mass density of a spherical galaxy varies as $${K \over r}$$ over a large distance ‘r’ from its centre. In that region, a small star is in a circular orbit of radius R. Then the period of revolution, T depends on R as :

If speed V, area A and force F are chosen as fundamental units, then the dimension of Young’s modulus will be