A solid sphere of mass $2\mathrm{kg}$ is resting inside a cube as shown in figure. The cube is moving with a velocity $\overrightarrow{v}=\left(5t\hat{i}+2t\hat{j}\right) \mathrm{m} {\sec }^{-1}$. Here $t$ is the time in second. All surface are smooth. The sphere is at rest with respect to the cube. The total force exerted by sphere on the cube is $a\hat{i}+b\hat{j}$ Nuwton. Value of $\frac{b}{a}$ is

 

If contact force between $2\mathrm{kg}$ and $4\mathrm{kg}$ is $f_1$ and between $4\mathrm{kg}$ and $6\mathrm{kg}$ is $f_2$. Find out $\frac{f_1}{f_2}$.

Two blocks of mass $2.9\mathrm{kg}$ and $1.9\mathrm{kg}$ are suspended from a rigid support $S$ by two inextensible wires each of length $1\mathrm{m}$ (see figure). The upper wire has negligible mass and the lower wire has a uniform mass of $0.2{\mathrm{kgm}}^{-1}$. The whole system of blocks, wires and support have an upward acceleration of $0.2 {\mathrm{ms}}^{-2}$. The acceleration due to gravity is $9.8{\mathrm{ms}}^{-2}$. IF the tension at the midpoint of the lower and upper wires are $T_1$ and $T_2$ respectively. Find value of $\frac{T_2}{T_1}$

A dynamometer is attached to two blocks of masses $6\mathrm{kg}$ and $4\mathrm{kg}$. Forces of $20\mathrm{N}$ and $10\mathrm{N}$ are applied on the blocks as shown in figure. The dynamometer reading is given as $x \mathrm{N}$. Find the value of $x$.

Two block of mass $8\mathrm{kg}$ and $4\mathrm{kg}$ are connected by a string as shown. They are initially at rest on the floor, when a force of $100\mathrm{N}$ is applied on the pulley in upward direction. If acceleration of the blocks are $a_1$ and $a_2$, find value of $\left(a_1+a_2\right) \left(g=10{\mathrm{ms}}^{-2}\right)$

Find force in newton which mass $A$ exerts on mass $B$ if $B$ is moving towards right with $3{\mathrm{ms}}^{-2}$. All surfaces are smooth and $g=10{\mathrm{ms}}^{-2}$

A system of two blocks and a light string are kept on two inclined faces (rough) as shown in the figure below. All the required data are mentioned in the diagram. Pulley is light and frictionless. (Take $g=10{\mathrm{ms}}^{-2}, \sin 37°=3/5$) If the system is released from rest then what is the range of the tension in the string?