Two blocks of equal masses are connected with a massless spring of spring constant $k = 2500 \,N/m$ and natural length $10 \,cm$,resting on a frictionless horizontal plane. If a constant horizontal force $F = 10 \,N$ is applied as shown in the figure,find the maximum distance between the blocks. (in $cm$)

State whether the following statements are true or false:
$(a)$ Momentum and the change in momentum are always in the same direction.
$(b)$ Action force and reaction force always act simultaneously and on the same body.
$(c)$ The maximum static frictional force depends on the area of the contact surface.

$A$ bird is sitting in a large closed cage which is placed on a spring balance. It records a weight of $25 \, N$. The bird (mass $m = 0.5 \, kg$) flies upward in the cage with an acceleration of $2 \, m/s^2$. The spring balance will now record a weight of ........ $N$.

If $M_2 = 2M_1$ and $\theta = 30^\circ$,the acceleration of $M_2$ is $a$. If the positions of the blocks are interchanged,what will be the acceleration of $M_2$?

$A$ body of mass $2 \ kg$ is initially at rest. It moves on a table under the influence of a horizontal force of $7 \ N$. If the coefficient of kinetic friction is $0.1$,then the work done by the applied force and the work done by the frictional force in $10 \ s$ are respectively:

Two pulley arrangements shown in the figure are identical. The mass of the rope is negligible. In figure $(a)$,the mass $m$ is lifted by attaching a mass $2m$ to the other end of the rope. In figure $(b)$,$m$ is lifted up by pulling the other end of the rope with a constant downward force $F = 2mg$. The accelerations of $m$ in the two cases are respectively: