Three blocks of masses $m_1=4 \, kg$, $m_2=2 \, kg$, and $m_3=4 \, kg$ are connected with ideal strings passing over a smooth, massless pulley as shown in the figure. The acceleration of the blocks will be ......... $m/s^2$ $(g=10 \, m/s^2)$.

Objects $A$ and $B$,each of mass $m$,are connected by a light inextensible cord. They are constrained to move on a frictionless ring in a vertical plane as shown in the figure. The objects are released from rest at the positions shown. The tension in the cord just after release will be

The same spring is attached to $2 \ kg, 3 \ kg$ and $1 \ kg$ blocks in three different cases as shown in the figure. If $x_1, x_2$ and $x_3$ are the extensions in the spring in these cases,respectively,find the correct relation between them.

Two masses $m_1 = 5\,kg$ and $m_2 = 4.8\,kg$ tied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when they are free to move (in $,m/s^2$)? $(g = 9.8\,m/s^2)$

One end of a light string is fixed to a clamp on the ground and the other end passes over a fixed frictionless pulley as shown in the figure. It makes an angle of $30^{\circ}$ with the ground. The clamp can tolerate a vertical force of $40 \,N$. If a monkey of mass $5 \,kg$ were to climb up the rope,then the maximum acceleration in the upward direction with which it can climb safely is $\left(g=10 \,ms^{-2}\right)$ (in $\,ms^{-2}$)

Two identical blocks each of mass $M$ are attached to the ends of a massless inextensible string which passes over a pulley with a fixed axis as shown below. $A$ small mass $m$ is now placed on block $B$ (the right block). The acceleration with which the two blocks move together is ($g =$ gravitational acceleration).