An infinite number of masses are placed on a frictionless table and they are connected via massless strings. Their masses follow the sequence $m, \frac{m}{2}, \frac{m}{6}, \ldots, \frac{m}{n!}, \ldots$ and they are further connected to a mass $m$ that hangs over a massless pulley. The acceleration of the hanging mass is

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 ........ $^o$.

On which factors does the stopping distance of a vehicle depend?

$A$ force of $36 \, \text{dyne}$ acts on a body placed on an inclined plane making an angle of $60^{\circ}$ with the horizontal. If the mass of the body is $18 \, \text{g}$,what is the acceleration of the body in the horizontal direction?

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 $A$ of mass $m_1$ rests on a horizontal table. $A$ light string connected to it passes over a frictionless pulley at the edge of the table,and from its other end,another block $B$ of mass $m_2$ is suspended. The coefficient of kinetic friction between the block $A$ and the table is $\mu_k$. When the block $A$ is sliding on the table,the tension in the string is: