An elevator weighing $6000\,kg$ is pulled upward by a cable with an acceleration of $5\,ms^{-2}$. Taking $g$ to be $10\,ms^{-2}$,the tension in the cable is ............ $N$.

Two masses of $4\, kg$ and $5 \,kg$ are connected by a string passing through a frictionless pulley and are kept on a frictionless table as shown in the figure. The acceleration of the $5\, kg$ mass is ........... $m/s^2$.

$A$ string tied to a roof can bear a maximum tension of $50 \,kg$ wt. The minimum acceleration with which a man of $98 \,kg$ can descend is ...... $m/s^2$ [Take $g = 9.8 \,m/s^2$].

Two masses $A$ and $B$,each of mass $M$,are connected by a massless spring. $A$ force $F$ acts on the mass $B$ as shown in the figure. If the mass $A$ starts moving away from mass $B$ with acceleration $a$,then the acceleration of mass $B$ will be:

The figure shows a uniform rod of length $30 \,cm$ having a mass of $3.0 \,kg$. The rod is pulled by constant forces of $20 \,N$ and $32 \,N$ as shown. Find the force exerted by the $20 \,cm$ part of the rod on the $10 \,cm$ part (all surfaces are smooth).

$A$ man slides down a light rope whose breaking strength is $\eta$ times the weight of the man $(\eta < 1)$. What is the maximum acceleration of the man so that the rope does not break?