A block of mass $5\, kg$ is $(i)$ pushed in case $(A)$ and $(ii)$ pulled in case $(B)$, by a force $F = 20\, N$, making an angle of $30^o$ with the horizontal, as shown in the figures. The coefficient of friction between the block and floor is $\mu = 0.2$. The difference between the accelerations of the block, in case $(B)$ and case $(A)$ will be ........ $ms^{-2}$ .$(g = 10\, ms^{-2})$

A child weighing $25$ kg slides down a rope hanging from the branch of a tall tree. If the force of friction acting against him is $2\, N$,  ........ $m/s^2$ is the acceleration of the child (Take $g = 9.8\,m/{s^2})$

Maximum value of static friction is called

A block weighs $W$ is held against a vertical wall by applying a horizontal force $F$. The minimum value of $F$ needed to hold the block is $[\mu < 1]$

A block of mass $m$ is in contact with the cart $C$ as shown in the figure. The coefficient of static friction between the block and the cart is $\mu .$ The acceleration $\alpha$ of the cart that will prevent the block from falling satisfies

Two balls of masses ${m_1}$ and ${m_2}$ are separated from each other by a powder charge placed between them. The whole system is at rest on the ground. Suddenly the powder charge explodes and masses are pushed apart. The mass ${m_1}$ travels a distance ${s_1}$ and stops. If the coefficients of friction between the balls and ground are same, the mass ${m_2}$ stops after travelling the distance