The current $${\rm I}$$ drawn from the $$5$$ volt source will be

A thin circular ring of mass $$m$$ and radius $$R$$ is rotating about its axis with a constant angular velocity $$\omega $$. Two objects each of mass $$M$$ are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity $$\omega ' = $$

A particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity 'v' that varies as $$v = \alpha \sqrt x $$. The displacement of the particle varies with time as

A mass of $$M$$ $$kg$$ is suspended by a weightless string. The horizontal force that is required to displace it until the string makes an angle of $${45^ \circ }$$ with the initial vertical direction is