Three blocks of masses $4\, kg, 8\,kg$ and $24 \,kg$ are connected to each other with light strings and placed on a smooth horizontal floor as shown in figure. If the system moves with an acceleration of $2\, ms^{-2}$, the applied force $F$ is ............ $N$
$36$
$72$
$18$
$108$
A block '$A$' takes $2\,s$ to slide down a frictionless incline of $30^{\circ}$ and length ' $l$ ', kept inside a lift going up with uniform velocity ' $v$ '. If the incline is changed to $45^{\circ}$, the time taken by the block, to slide down the incline, will be approximately $........\,s$
Two particle of mass $m$ each are tied at the ends of a light string of length $2 \mathrm{a}$. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance $'a'$ from the center $\mathrm{P}$ (as shown in the figure). Now, the mid-point of the string is pulled vertically upwards with a small but constant force $F$. As a result, the particles move towards each other on the surface. The magnitude of acceleration, when the separation between them becomes $2 \mathrm{x}$ is
Three identical blocks of masses $m=2\; k g$ are drawn by a force $F=10.2\; N$ with an acceleration of $0.6\; ms ^{-2}$ on a frictionless surface, then what is the tension (in $N$) in the string between the blocks $B$ and $C$?
A uniform rope of mass $1.0\, kg$ is connected with a box of mass $2.0\, kg$, which is placed on a smooth horizontal surface. The free end of the rope is pulled horizontally by a force $6\, N$. Find the tension at the midpoint of the rope ....... $N$