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 :-

- A
$\frac{\mu mg}{K}$

- B
$\frac{2 \mu mg}{K}$

- C
$\frac{\mu g}{K}$

- D
$\frac{k}{\mu mg}$

A ball is dropped from a height of $20\, cm$. Ball rebounds to a height of $10\, cm$. What is the loss of energy ? ................ $\%$

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?

- [JEE MAIN 2019]

$A$ hemisphere of mass $3m$ and radius $R$ is free to slide with its base on a smooth horizontal table. $A$ particle of mass $m$ is placed on the top of the hemisphere. If particle is displaced with a negligible velocity, then find the angular velocity of the particle relative to the centre of the hemisphere at an angular displacement $\theta$ , when velocity of hemisphere is $v$.

A mass of $M\ kg$ is suspended by a weightless string. The horizontal force that is displace it until the string makes an angle of $45^o $ with the initial vertical direction is

- [AIEEE 2006]

A particle is released from a height $H$. At a certain height its kinetic energy is two times its potential energy. Height and speed of particle at that instant are