$A$ spring of force constant $k$ is cut into two pieces such that one piece is three times the length of the other. The longer piece will have a force constant of

$A$ mass of $10 \ kg$ is suspended from a spring balance. It is pulled aside by a horizontal string so that it makes an angle of $60^{\circ}$ with the vertical. The new reading of the balance is

Infinite springs with force constants $k$,$2k$,$4k$,$8k$,... respectively are connected in series. The effective force constant of the system will be:

Two masses of $10 \, kg$ and $20 \, kg$ respectively are connected by a massless spring as shown in the figure. $A$ force of $200 \, N$ acts on the $20 \, kg$ mass. At the instant shown,the $10 \, kg$ mass has an acceleration of $12 \, m/s^2$ towards the right. The acceleration of the $20 \, kg$ mass at this instant is ........ $m/s^2$.

$A$ block of mass $M$ is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has a force constant $k$. The mass is released from rest with the spring initially unstretched. The maximum extension produced in the length of the spring will be

When a $1.0\,kg$ mass hangs attached to a spring of length $50\,cm$,the spring stretches by $2\,cm$. The mass is pulled down until the length of the spring becomes $60\,cm$. What is the amount of elastic energy stored in the spring in this condition,if $g = 10\,m/s^2$? (in $Joule$)