Give an example of a variable force. Write the formula for Hooke's law.

$A$ spring has a spring constant $k$ and original length $l$. If it is cut into pieces in the ratio $\alpha : \beta : \gamma$,find the spring constant of each piece in terms of the original spring constant $k$ (where $\alpha, \beta$,and $\gamma$ are integers).

$A$ small block of mass $100\,g$ is tied to a spring of spring constant $7.5\,N/m$ and natural length $20\,cm$. The other end of the spring is fixed at a point $A$. If the block moves in a circular path on a smooth horizontal surface with a constant angular velocity of $5\,rad/s$ about point $A$,then the tension in the spring is $.........\,N$.

$A$ uniform spring of force constant $k$ is cut into two pieces,the lengths of which are in the ratio $1 : 2$. The ratio of the force constants of the shorter and the longer pieces is

The tension in the spring is

$A$ bead of mass $m = 100 \,g$ is attached to one end of a spring of natural length $L$ and spring constant $k = \frac{(\sqrt{3}+1) mg}{L}$. The other end of the spring is fixed at point $A$ on a smooth vertical ring of radius $R$. The bead is at point $B$ such that the spring makes an angle of $30^{\circ}$ with the horizontal diameter. The normal reaction at $B$ just after it is released to move is (take $g = 9.8 \,ms^{-2}$): (in $\,N$)