The ring shown in figure is given a constant horizontal acceleration $(a_0=\frac{g}{\sqrt{3}})$. The maximum deflection of the string from the vertical is ${\theta }_0$. Then

In the given figure, a small block of mass $m$ is kept on the block of mass $M$. Then

A block of mass $m$ is placed on a wedge. The wedge can be accelerated in four manners marked as $\left(1\right), \left(2\right), \left(3\right)$ and $\left(4\right)$ as shown in figure. If the normal reactions in situations $\left(1\right), \left(2\right), \left(3\right)$ and $\left(4\right)$ are $N_{1^{,}}{N}_2, N_{3,}$ and $N_4,$, respectively and acceleration with which the block slides on the wedge in the situations are $b_1, b_2, b_3,$ and $b_4$, respectively. Then

Seven pulleys are connected with the help of three light strings as shown in figure. Consider $P_3,P_4,P_5$ as light pulleys and pulleys $P_6$ and $P_7$ have masses $m$ each. For this arrangement, mark the correct statement$\left(s\right)$.

In the figure shown, $A$ and $B$ are free to move. All the surfaces are smooth. Then $(0<\theta <{90}^{°})$

Two blocks of masses $m_1=2 \mathrm{kg}$ and $m_2=4 \mathrm{kg}$ hang over a massless pulley as shown in the figure. A force $F_0=100 \mathrm{N}$ acting at the axis of the pulley accelerates the system upwards. Then

In the figure below, all surfaces are smooth, string is light and pulley is frictionless. Mark the correct statement$\left(s\right)$.

For given figure, $m_A$ is $30 \mathrm{kg}, m_B=m_C=5 \mathrm{kg},$ respectively. All contact surfaces are smooth $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$. Select the correct statement $\left(s\right)$.

For the system shown in figure, all the pulleys are light and frictionless and strings are ideal. Initially the system is held at rest by some external means. Now, the system is released i.e., external effect has been removed, but still it has been observed that $10 \mathrm{kg}$ and $5 \mathrm{kg}$ blocks are not moving. This is possible when