A spring-mass system vibrates such that mass travel on surface of coefficient of friction $\mu$. Mass is released after compressing the spring by distance a and it travels upto distance $b$ after its equilibrium position, then travelling from $x = -a$ to $x = b$ the reduction in its amplitude will be :-
$\frac{\mu mg}{K}$
$\frac{2 \mu mg}{K}$
$\frac{\mu g}{K}$
$\frac{k}{\mu mg}$
A uniform chain of length $2\,m$ is kept on a table such that a length of $60\,cm$ hangs freely from the edge of the table. The total mass of the chain is $4\,kg$. What is the work done in pulling the entire chain on the table ................ $\mathrm{J}$
The potential energy in joules of a particle of mass $1\, kg$ moving in a plane is given by $U = 3x + 4y$, the position coordinates of the point being $x$ and $y$, measured in metres. If the particle is initially at rest at $(6,4)$, then
A uniform chain (mass $M,$ length $L$) is released from rest from a smooth horizontal surface as shown in the figure. Velocity of the chain at the instant it completely comes out of the table will be
Two inclined planes are placed as shown in figure.
A block is projected from the Point $A$ of inclined plane $A B$ along its surface with a velocity just sufficient to carry it to the top Point $B$ at a height $10 m$. After reaching the Point $B$ the block slides down on inclined plane $BC$. Time it takes to reach to the point $C$ from point $A$ is $t (\sqrt{2}+1) s$. The value of $t$ is........(use $g =10 m / s ^{2}$ )
A $2\ kg$ object is floating at rest, acted upon by only force as indicated in figure. Find the total work done by the force in $3\ sec$ ..................... $\mathrm{J}$