A wire elongates by $$l$$ $$mm$$ when a LOAD $$W$$ is hanged from it. If the wire goes over a pulley and two weights $$W$$ each are hung at the two ends, the elongation of the wire will be (in $$mm$$)

A ball of mass $$0.2$$ $$kg$$ is thrown vertically upwards by applying a force by hand. If the hand moves $$0.2$$ $$m$$ while applying the force and the ball goes upto $$2$$ $$m$$ height further, find the magnitude of the force. (consider $$g = 10\,m/{s^2}$$).

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