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 :-
$\frac{\mu mg}{K}$
$\frac{2 \mu mg}{K}$
$\frac{\mu g}{K}$
$\frac{k}{\mu mg}$
Consider an elliptically shaped rail $P Q$ in the vertical plane with $O P=3 \ m$ and $OQ =4 \ m$. A block of mass $1 \ kg$ is pulled along the rail from $P$ to $Q$ with a force of $18 \ N$, Which is always parallel to line $PQ$ (see the figure given). Assuming no frictional losses, the kinetic energy of the block when it reaches $Q$ is $(n \times 10)$ joules. The value of $n$ is (take acceleration due to gravity $=10 \ ms ^{-2}$ )
Two monkeys with the same mass stand on a branch at height $h$ above the horizontal jungle floor. Monkey $A$ steps off the branch holding the end of an inextensible rope of length $L$ whose other end is tied to another branch at height $H$, lets go at the bottom of the swing, and falls freely to the floor, as shown below. Monkey $B$ steps off and falls straight downward. Then, neglecting air resistance but not the tension in the rope, the total work $W$ done on each monkey and the speed $v$ with which each hits the floor are as follows:
A small box resting on one edge of the table is struck in such a way that it slides upto the other edge, $1 \,m$ away after $2 \,s$. The coefficient of kinetic friction between the box and the table
A particle which is experiencing a force, given by $\vec F = 3\vec i -12\vec j$, undergoes a displacement of $\vec d = 4\vec i$ . If the particle had a kinetic energy of $3\, J$ at the beginning of the displacement, what is its kinetic energy at the end of the displacement?
A bungee jumper is jumping with help of elastic ideal rope (Force constant $K$). Jumper steps off the bridge and falls from the rest towards the river below. He does not hit the water. The mass of jumper is $m$, natural length of rope is $l$. Gravity is $g$, assume every thing ideal. then, choose the incorrect option