A spring of force constant k is cut into two pieces such that one piece is double the length of the other. Then the long piece will have a force constant of

A block of mass $5 \mathrm{kg}$, resting on a horizontal surface, is connected by a cord, passing over a light frictionless pulley to a hanging block of mass $5 \mathrm{kg}$. The coefficient of kinetic friction between the block and the surface is $0.5$. Tension in the cord is [Take $\mathrm{g}=9.8\mathrm{ }\mathrm{m} {\mathrm{s}}^{-2}$]

Two blocks of masses $m_1$ and $m_2$ connected by a string are placed gently over a fixed inclined plane, such that the tension in the connecting string is initially zero. The coefficient of the friction between $m_1$ and inclined plane is ${\mu }_1$, between $m_2$ and the inclined plane is ${\mu }_2$. The tension in the string shall remain zero if