The springs shown are identical. When $A = 4kg$, the elongation of spring is $1\, cm$. If $B = 6\,kg$, the elongation produced by it is  ..... $ cm$

Two particles of mass $m$ are constrained to move along two horizontal frictionless rails that make an angle $2\theta $ with respect to each other. They are connected by a spring with spring constant $k$ . The angular frequency of small oscillations for the motion where the two masses always stay parallel to each other (that is the distance between the meeting point of the rails and each particle is equal) is 

$A$ block of mass $M_1$ is hanged by a light spring of force constant $k$ to the top bar of a reverse Uframe of mass $M_2$ on the floor. The block is pooled down from its equilibrium position by $a$ distance $x$ and then released. Find the minimum value of $x$ such that the reverse $U$ -frame will leave the floor momentarily.

When a mass $m$ is attached to a spring, it normally extends by $0.2\, m$. The mass $m$ is given a slight addition extension and released, then its time period will be

A block $P$ of mass $m$ is placed on a smooth horizontal surface. A block $Q$ of same mass is placed over the block $P$ and the coefficient of static friction between them is ${\mu _S}$. A spring of spring constant $K$ is attached to block $Q$. The blocks are displaced together to a distance $A$ and released. The upper block oscillates without slipping over the lower block. The maximum frictional force between the block is

Define simple pendulum and the length of pendulum.