The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium,the angle $\theta$ should be ........ $^o$.

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 $M_2$?

$A$ block of mass $M$ is placed on a horizontal surface and is tied with an inextensible string to a block of mass $m$,as shown in the figure. $A$ block of mass $m_0$ is also placed on $M$. The surface under $M$ is smooth,while the vertical surface under $m$ is rough with a coefficient of friction $\mu$. The minimum value of $\mu$ for which the block $m$ remains stationary is:

$A$ metal block is resting on a rough wooden surface. $A$ horizontal force applied to the block is increased uniformly with time, given by $F = kt$. Which of the following curves correctly represents the velocity of the block as a function of time?

Two blocks $1$ and $2$ of equal mass $m$ are connected by an ideal string over a frictionless pulley. The blocks are attached to the ground by springs having spring constants $k_1$ and $k_2$ such that $k_1 > k_2$. Initially,both springs are unstretched. Block $1$ is slowly pulled down a distance $x$ and released. Just after the release,the possible values of the magnitudes of the accelerations of the blocks $a_1$ and $a_2$ can be

$A$ block of mass $m$ moves on a horizontal rough surface with initial velocity $v$. The height of the centre of mass of the block is $h$ from the surface. Consider a point $A$ on the surface.