Two blocks $A$ and $B$ of equal mass $2\mathrm{kg}$ are arranged as shown with springs $S_1$ and $S_2$. Spring $S_2$ is pulled with force $F=6 \mathrm{N}$. Acceleration of block $B$ is $4 \mathrm{m} {\mathrm{s}}^{-2}$ towards right at an instant. If $F$ is suddenly removed at this instant, the instantaneous acceleration of $A$ and $B$ will be (assume no friction)

A mass $m$ is attached to two springs as shown in figure. The spring constants of two springs are $K_1$ and $K_2.$ For the frictionless surface, the time period of oscillation of mass $m$ is

Two blocks $A$ and $B$ are placed one over the other on a smooth horizontal surface. The maximum horizontal force that can be applied on lower block $A$, so that $A$ and $B$ move without separation is $49 \mathrm{N}$. The coefficient of friction between $A$ and $B$ is

The length of a metal wire is ${\ell }_1,$ when the tension in it is $T_1$ and is ${\ell }_2$ when the tension is $T_2.$ The natural length of the wire is:

Two identical springs are connected to mass$m$ as shown $(k=\text{spring constant})$ . If the period of the configuration in (i) is $2 \mathrm{s}$, the period of the configuration (ii) is:

I 

II 

A boy throws a cricket ball from the boundary to the wicket keeper. If the frictional force due to air $\left(f_a\right)$ cannot be ignored, the forces acting on the ball at the position $X$ are represented by

A maximum of $3 \mathrm{N}$ force can be applied on a block, down the incline, that would still not move the block which is placed on a rough inclined plane as shown in the figure. The maximum external force up the inclined plane that does not move the block is $12 \mathrm{N}$. The coefficient of static friction between the block and the plane is $\left[\mathrm{Take} g=10 \mathrm{m} {\mathrm{s}}^{-2}\right]$

As shown in the figure, an iron block $A$ of volume $0.25 {\mathrm{m}}^3$ is attached to a spring $S$ of unstretched length $1.0 \mathrm{m}$ and hanging to the ceiling of a roof. The spring gets stretched by $0.2 \mathrm{m}$. This block is removed and another block $B$ of iron of volume $0.75 {\mathrm{m}}^3$ is now attached to the same spring and kept on a frictionless incline plane of $30°$ inclination. The distance of the block from the top along the incline at equilibrium is

A block of mass $20 \mathrm{kg}$ is suspended through two spring balances with negligible mass as shown in figure. What will be the readings in the upper and lower balance respectively ?