Two boys of masses $10 \mathrm{kg}$ and $8 \mathrm{kg}$ are moving along a vertical rope, the former climbing up with the acceleration of $2 \mathrm{m} {\mathrm{s}}^{-2}$ while the later coming down with a uniform velocity of $2 \mathrm{m} {\mathrm{s}}^{-1}$. Then tension in the rope at the fixed support is  (Take $g = 10 \mathrm{m} {\mathrm{s}}^{-2}$ )

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