A particle of mass $\mathrm{m}$ is made to move with uniform speed $v_0$ along the perimeter of a regular hexagon, inscribed in a circle of radius $R$. The magnitude of impulse applied at each corner of the hexagon is:-

In the figure shown the acceleration of $A$is,${\overrightarrow{a}}_A=15\hat{\mathrm{i}}+15\hat{\mathrm{j}}$ then the acceleration of $B$ is ($A$ remains in contact with $B$)

Block $B$ has a downward velocity in $m{s}^{-1}$ and given by $v_B=\frac{t^2}{2}+\frac{t^3}{6},$ where $t$ is in $s$. Acceleration of $A$ at $t=2 \mathrm{second}$ is 

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 $g= 10 \mathrm{m} {\mathrm{s}}^{-2}$):