$A$ $1.0\, kg$ block collides with a horizontal weightless spring of force constant $2.75 Nm^{-1}$ as shown in figure. The block compresses the spring $4.0\, m$ from the rest position. If the coefficient of kinetic friction between the block and horizontal surface is $0.25$, the speed of the block at the instant of collision is ................. $\mathrm{m}/ \mathrm{s}^{-1}$
$0.4 $
$4$
$0.8$
$8 $
A block of mass $m = 0.1\,kg$ is connected to a spring of unknown spring constant $k.$ It is compressed to a distance $x$ from its equilibrium. position and released from rest . After approaching half the distance $(\frac {x}{2})$ from equilibrium position, it hits another block and comes to rest momentarily, while the other block moves with a velocity $3\,ms^{-1}.$ The total initial energy of the spring 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
Two block of masses $m_1$ and $m_2$ connected with the help of a spring of spring constant $k$ initially to natural length as shown. A sharp impulse is given to mass $m_2$ so that it acquires a velocity $v_0$ towards right. If the system is kept an smooth floor then find the maximum elongation that the spring will suffer
A mass of $1\, kg$ is hanging from a spring of spring constant $1\, N/m$. If Saroj pulls the mass down by $2\,m$. The work done by Saroj is......$J$
A uniform solid cylinder of mass $M = 3\ kg$ and radius $R = 10\ cm$ is connected about an axis through the cnetre of the cylinder to a horizontal spring with spring constant $8\ N/m$.The cylinder is pulled back, stretching the spring $1\,m$ from equilibrium.When released, the cylinder rolls without slipping. What is the speed of the center of th ecylinder when it returns to equilibrium? .................. $m/s$