If a spring extends by $x$ on loading then energy stored by the spring is ($T$ is tension in spring, $K$ is spring constant)
$\frac{{{T^2}}}{{2x}}$
$\frac{{{T^2}}}{{2K}}$
$\frac{{2K}}{{{T^2}}}$
$\frac{{2{T^2}}}{K}$
A force $\overrightarrow F = (5\hat i + 3\hat j)$Newton is applied over a particle which displaces it from its origin to the point $\overrightarrow r = (2\hat i - 1\hat j)$ metres. The work done on the particle is..............$J$
A body of mass $2\, kg$ slides down a curved track which is quadrant of a circle of radius $1$ $meter$ as shown in figure. All the surfaces are frictionless. If the body starts from rest, its speed at the bottom of the track is ............. $\mathrm{m}/ \mathrm{s}$
Pulley and spring are massless and the friction is absent everwhere. $5\,kg$ block is released from rest. The speed of $5\,kg$ block when $2\,kg$ block leaves the contact with ground is (take force constant of the spring $K = 40\,N/m$ and $g = 10\,m/s^2$ )
Work done in time $t $ on a body of mass $m$ which is accelerated from rest to a speed $v$ in time ${t_1}$ as a function of time $t$ is given by
A mass of $0.5\, kg$ moving with a speed of $1.5\, m/s$ on a horizontal smooth surface, collides with a nearly weightless spring of force constant $k=50\,N/m$. The maximum compression of the spring would be ................. $\mathrm{m}$