A block of mass $m$ is pushed against a spring whose spring constant is $k$ fixed at one end with a wall. The block can slide on a frictionless table as shown in figure. If the natural length of spring is $L_0$ and it is compressed to half its length when the block is released, find the velocity of the block, when the spring has natural length
$\sqrt {\frac{m}{k}} .\frac{{{L_0}}}{2}$
$\sqrt {\frac{k}{m}} .\frac{{{L_0}}}{2}$
$\sqrt {\frac{k}{m}} .{L_0}$
$\sqrt {\frac{{k{L_0}}}{m}} $
Initially spring is in natural length and both blocks are in rest condition. Then determine Maximum extension is spring. $k=20 N / M$
$A$ small block of mass $m$ is placed on $a$ wedge of mass $M$ as shown, which is initially at rest. All the surfaces are frictionless . The spring attached to the other end of wedge has force constant $k$. If $a'$ is the acceleration of $m$ relative to the wedge as it starts coming down and $A$ is the acceleration acquired by the wedge as the block starts coming down, then Maximum velocity of $M$ is:
The potential energy of a weight less spring compressed by a distance $ a $ is proportional to
A $1\; kg$ block situated on a rough incline is connected to a spring of spring constant $100\;N m ^{-1}$ as shown in Figure. The block is released from rest with the spring in the unstretched position. The block moves $10 \;cm$ down the incline before coming to rest. Find the coefficient of friction between the block and the incline. Assume that the spring has a negligible mass and the pulley is frictionless.
A ball is dropped from a height of $80\,m$ on a surface which is at rest. Find the height attainded by ball after $2^{nd}$ collision if coefficient of restitution $e = 0.5$ ............ $\mathrm{m}$