$A$ 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

Two balls $A$ and $B$ of masses $100 \ gm$ and $250 \ gm$ are connected by a stretched massless spring and placed on a smooth table. When the balls are released simultaneously,the initial acceleration of ball $B$ is $10 \ cm/s^2$ towards the west. Find the magnitude and direction of the initial acceleration of ball $A$.

$A$ spring of force constant $k$ is cut into three equal parts. The force constant of each part would be

Two springs having spring constants $k_1$ and $k_2$ are connected in series,their resultant spring constant is $2 \text{ unit}$. If they are connected in parallel,their resultant spring constant is $9 \text{ unit}$. Find the values of $k_1$ and $k_2$.

Two springs of spring constants $1500 \ N/m$ and $3000 \ N/m$ respectively are stretched with the same force. They will have potential energy in the ratio

In the setup shown,a $200\, N$ block is supported in equilibrium with the help of strings and a spring. At point $O$,the strings are knotted. The extension in the spring is $4\, cm$. The force constant of the spring is closest to ............ $N/m$ $[g = 10\, m/s^2]$.