A block of mass $1 \mathrm{kg}$ is held at rest against a rough vertical surface by pushing by a force $F$ horizontally. The coefficient of friction is $0.5$ when

The system is pushed by a force $F$ as shown in figure. All surface are smooth except between $B$ and $C$. Friction coefficient between $B$ and $C$ is $\mu$. Minimum value of $F$ to prevent block $B$ from downward slipping is

In figure shown, both blocks are released from rest. The time to cross each other is

If masses are released from the position shown in figure then time elapsed before mass $m_1$ collides with the floor will be:

Same spring is attached with $2 \mathrm{kg}, 3 \mathrm{kg}$ and $1 \mathrm{kg}$ blocks in three different case as shown in figure. If $x_1, x_2$ and $x_3$ be the extension in the spring in these three case then

A block $A$ of mass $m$ is placed over a plank $B$ of mass $2 \mathrm{m}$. Plank $B$ is placed over a smooth horizontal surface. The coefficient of friction between $A$ and $B$ is $0.5$. Block $A$ is given a velocity $v_0$ towards right. Acceleration of $B$ relative to $A$ is

Block $A$ of mass $m$ is placed over a wedge $B$ of same mass  $\mathrm{m}$. Assuming all surface to be smooth. The displacement of block $A$ in $1 \mathrm{s}$ if the system is released from rest is

A man of mass $50 \mathrm{kg}$ is pulling on a plank of mass $100 \mathrm{kg}$ kept on a smooth floor as shown with force of $100 \mathrm{N}$. both man & plank move together, find force of friction acting on man.

In the following arrangement the system is initially at rest. The $5 \mathrm{kg}$ block is now released. Assuming the pulleys and string to be massless and smooth, the acceleration of blocks is