$A$ horizontal force of $10 \,N$ is applied to a block $A$ as shown in the figure. The masses of blocks $A$ and $B$ are $2 \,kg$ and $3 \,kg$ respectively. The blocks slide over a frictionless surface. The force exerted by block $A$ on block $B$ is:

$A$ monkey of mass $20\,kg$ is holding a vertical rope. The rope will not break when a mass of $25\,kg$ is suspended from it but will break if the mass exceeds $25\,kg$. What is the maximum acceleration with which the monkey can climb up along the rope in $m/s^2$? (Take $g = 10\,m/s^2$)

Two particles of equal mass $m$ are connected to a rope $AB$ of negligible mass such that one is at end $A$ and the other divides the length of the rope in the ratio $1:2$ from $B$. The rope is rotated about end $B$ in a horizontal plane. The ratio of the tension in the smaller part (between $B$ and the middle particle) to the tension in the larger part (between the two particles) is (ignore the effect of gravity).

What will be the acceleration of the system and tension in the rope connecting $5\,kg$ and $1\,kg$ blocks?

$A$ uniform thick string of length $8\, m$ is resting on a horizontal frictionless surface. It is pulled by a horizontal force of $8\, N$ from one end. The tension in the string at $3\, m$ from the force applied is ........ $N$.

$A$ block of mass $m$ slides down on a wedge of mass $M$ as shown in the figure. Let $\vec a_1$ be the acceleration of the wedge and $\vec a_2$ be the acceleration of the block with respect to the ground. $N_1$ is the normal reaction between the block and the wedge,and $N_2$ is the normal reaction between the wedge and the ground. Friction is absent everywhere. Select the incorrect alternative.