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,

A toy gun fires a plastic pellet with a mass of $0.5\  g$. The pellet is propelled by a spring with a spring constant of $1.25\  N/cm$, which is compressed $2.0\  cm$ before firing. The plastic pellet travels horizontally $10\  cm$ down the barrel (from its compressed position) with a constant friction force of $0.0475\  N$. What is the speed (in $SI\  units$) of the bullet as it emerges from the barrel?

As shown in figure, two blocks are connected with a light spring. When spring was at its natural length, velocities are given to them as shown in figure. Choose the wrong alternative.

Two masses $A$ and $B$ of mass $M$ and $2M$ respectively are connected by a compressed ideal spring. The system is placed on $a$ horizontal frictionless table and given $a$ velocity $u\, \hat k$ in the $z$ -direction as shown in the figure. The spring is then released. In the subsequent motion the line from $B$ to $A$ always points along the $\hat i$ unit vector. At some instant of $\rho$ time mass $B$ has $a$ $x$ -component of velocity as $V_x\, \hat i$ . The velocity ${\vec V_A}$ of as $A$ at that instant is

Initially spring in its natural length now a block at mass $0.25 \,kg$ is released than find out maximum force by system on floor ? (in $N$)