A long spring, when stretched by a distance $x,$ has the potential energy $u.$ On increasing the stretching to $nx.$ The potential energy of the spring will be
$\frac {u}{n}$
$nu$
$n^2u$
$\frac {u}{n^2}$
A rope is used to lower vertically a block of mass $M$ by a distance $x$ with a constant downward acceleration $\frac{g}{2}$. The work done by the rope on the block is
Two bodies with masses $M_1$ and $M_2$ have equal kinetic energies. If $p_1$ and $p_2$ are their respective momenta, then $p_1/p_2$ is equal to
The work done by a force $\vec F\, = \,( - \,6{x^3}\,\hat i)N$ , in displacing a particle from $x = 4\,m$ to $x = -\,2\,m$ is .............. $\mathrm{J}$
A vertical spring with force constant $K$ is fixed on a table. A ball of mass $m$ at a height $h$ above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance $d$. The net work done in the process is
System shown in figure is released from rest. Pulley and spring are massless and the friction is absent everywhere. The speed of $5\, kg$ block, when $2\, kg$ block leaves the contact with ground is (take force constant of the sprign $k = 40\, N/m$ and $g = 10\, m/s^2$)