A spring with spring constant k when stretched through $1\, cm$, the potential energy is $U$. If it is stretched by $4 \,cm.$ The potential energy will be
$4U$
$8U$
$16 U$
$2U$
A block of mass $\sqrt{2}\,kg$ is released from the top of an inclined smooth surface as shown in figure. If spring constant of spring is $100\,N / m$ and block comes to rest after compressing the spring by $1 \,m$, then the distance travelled by block before it comes to rest is ......... $m$
A body of mass $ 0.1 kg $ moving with a velocity of $10 m/s$ hits a spring (fixed at the other end) of force constant $ 1000 N/m $ and comes to rest after compressing the spring. The compression of the spring is .............. $\mathrm{m}$
A body of mass $1\,kg$ falls freely from a height of $100\,m,$ on a platform of mass $3\,kg$ which is mounted on a spring having spring constant $k = 1.25 \times 10^6\, N/m.$ The body sticks to the platform and the spring’s maximum compression is found to be $x.$ Given that $g = 10\,ms^{-2},$ the value of $x$ will be close to ................ $\mathrm{cm}$
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? .................. $m/s$
A block of mass $m$ slides from rest at a height $H$ on a frictionless inclined plane as shown in the figure. It travels a distance $d$ across a rough horizontal surface with coefficient of kinetic friction $\mu$ and compresses a spring of spring constant $k$ by a distance $x$ before coming to rest momentarily. Then the spring extends and the block travels back attaining a final height of $h$. Then,