If block $A$ is moving with an acceleration of $5{\mathrm{ms}}^{-2},$the acceleration of $B w.r.t.$ ground is 

 

In the figure acceleration of $A$ is $1{\mathrm{ms}}^{-2}$ upwards, acceleration of $B$is $7{\mathrm{ms}}^{-2}$ upward and acceleration of $C$ is $2{\mathrm{ms}}^{-2}$ upward. then acceleration of $D$ will be 

Block $A$and$C$ start from rest and move to the right with acceleration $a_A=12\mathrm{t} {\mathrm{ms}}^{-2}$ and $a_c=3{\mathrm{ms}}^{-2}.$ Here $t$ is in seconds. The time when block $B$ again comes to rest is

A light string fixed at one end to a clamp on ground passes over a fixed pulley and hangs at the other side. It makes an angle of $30°$ with the ground. A monkey of mass $5 \mathrm{kg}$ climbs up the rope. The clamp can tolerate a vertical force of $40 \mathrm{N}$ only. The maximum acceleration in upward direction with which the monkey can climb safely is (neglect friction and take $g= 10 \mathrm{m} {\mathrm{s}}^{-2}$):

For the system shown in the figure, the acceleration of the mass $m_4$ immediately after the lower thread $x$ is cut will be, (assume that the threads are weightless and inextensible, the spring are weightless, the mass of pulley is negligible and there is no friction)

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