A thin, uniform rod of mass $M$ and length $L$ is rotated with constant angular speed $\omega$ as shown in figure. Tension in the rod at position $A$ is

Two blocks of masses $10 \mathrm{kg}$ and $20 \mathrm{kg}$ are connected by a massless spring of spring constant $2000 \mathrm{N} {\mathrm{m}}^{-1}$ as shown in figure. A constant force of $200 \mathrm{N}$ acts on $20 \mathrm{kg}$ block. When the $10 \mathrm{kg}$  block has acceleration of $12 \mathrm{m} {\mathrm{s}}^{-2},$ the acceleration of $20 \mathrm{kg}$ block in $\mathrm{m} {\mathrm{s}}^{-2}$ is equal to

Two blocks $A$ and $B$ are connected through a string as shown in figure. If velocity of block $A$ is $5 \mathrm{m} {\mathrm{s}}^{-1}$ at given instant, then velocity of block $B$ (in $\mathrm{m} {\mathrm{s}}^{-1}$ ) at the same instant is given by (Given ${\theta }_1=60°,$${\theta }_2=37°,$ )

In figure shown, if the magnitude of acceleration of $m,$ is $2\sqrt{N} \mathrm{m} {\mathrm{s}}^{-2},$ given that the string is inextensible and the acceleration of $M$ is $2 \mathrm{m} {\mathrm{s}}^{-2}$ towards left, then find $N$

If hanging block is in equilibrium, then elongation in the spring in c.m. is equal to

In figure shown, pulleys are ideal. Initially the system is in equilibrium and string connecting $m_2$ to rigid support below is cut. What is the initial acceleration (in $\mathrm{m} {\mathrm{s}}^{-2}$) of  $m_2$? (Given $m_1=9 \mathrm{kg}; m_2=3 \mathrm{kg})$

In the arrangement shown in figure, the string and pulley are light. The car starts moving on the horizontal road with constant velocity $5 \mathrm{m} {\mathrm{s}}^{-1}$ towards left. Speed of $2 \mathrm{kg}$ block in $\mathrm{m} {\mathrm{s}}^{-1}$ when $\theta =60°$is

In the arrangement shown in figure the string and pulley are light. Value of$F$ (in $\mathrm{N}$ ) for which $4 \mathrm{kg}$ block will move with $1 \mathrm{m} {\mathrm{s}}^{-2}$ acceleration in the upward direction is