A slider block $A$ moves downward at a speed of $v_A = 2\ m/s$ , at an angle of $75^o$ with horizontal as shown in the figure. The velocity with respect to $A$ of the portion of belt $B$ between ideal pulleys $C$ and $D$ is $v_{CD/A} = 2\ m/s$ at an angle $\theta $ with the horizontal. The magnitude of velocity of portion $CD$ of the belt when $\theta = 15^o$ is .......... $m/s$
$2\sqrt 3$
$\sqrt {10} $
$2\sqrt 2$
$2$
If block $A$ is moving with an acceleration of $5\,m/s^2$, the acceleration of $B$ w.r.t. ground is
If pulleys shown in the diagram are smooth and massless and $a_1$ and $a_2$ are acceleration of blocks of mass $4 \,kg$ and $8 \,kg$ respectively, then
Three blocks $A, B$ and $C$ are suspended as shown in the figure. Mass of each blocks $A$ and $C$ is $m$. If system is in equilibrium and mass of $B$ is $M$, then :
Two masses $M _{1}$ and $M _{2}$ are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass $M _{2}$ is twice that of $M_{1}$. the acceleration of the system is $a_{1}$. When the mass $M_{2}$ is thrice that of $M_{1}$. The acceleration of The system is $a_{2}$. The ratio $\frac{a_{1}}{a_{2}}$ will be.