In one dimensional case, the relationship between force and position is shown in the figure. The work done by the force in displacing a body from $x = 1\, cm$ to $x = 5\, cm$ is ............ $\mathrm{ergs}$

A force of $\left( {2\hat i + 3\hat j + 4\hat k} \right)\,N$ acts on a body for $4\, sec$ and produces a displacement of $\left( {3\hat i + 4\hat j + 5\hat k} \right)\,m.$ The power used is ............. $\mathrm{W}$

A container of mass $m$ is pulled  by a constant force in which a second block of same mass $m$ is placed connected to the wall by a mass-less spring of constant $k$ . Initially the spring is in its natural length. Velocity of the container at the instant when compression in spring is maximum for the first time

A body constrained to move along $y-$ axis is subjected to a constant force $\vec F =  - \hat i + 2\hat j + 3\hat k\,N$ The work done by this force in moving the body a distance of $4\, m$ along $y-$ axis is ............... $\mathrm{J}$

A sphere is suspended by a thread of length $\ell $. What minimum horizontal velocity has to be imparted to the sphere for it to reach the height of the suspension

The length of a spring is $\alpha $ when a force of $4\,N$ is applied on it and the length is $\beta $ when $5\,N$ force is applied. Then the length of spring when $9\,N$ force is applied is