$A$ spring is compressed between two toy carts of masses $m_1$ and $m_2$. When the toy carts are released,the spring exerts equal and opposite forces for the same time $t$ on each toy cart. If the coefficients of friction $\mu$ between the ground and the toy carts are equal,then the ratio of the displacements of the toy carts is:

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

$A$ block is placed on a rough horizontal plane. $A$ time-dependent horizontal force $F = Kt$ acts on the block,where $K$ is a positive constant. The acceleration-time graph of the block is:

Fill in the blanks:
$(a)$ The friction acting on both wheels of a moving bicycle is in the ..... direction.
$(b)$ Friction depends on the ........... and ........ of the contact surfaces.
$(c)$ The necessary condition for parking a vehicle on a banked,curved road is ...........
$(d)$ The time rate of change of momentum gives the physical quantity ...........

Block $A$ of mass $m$ and block $B$ of mass $M$ are connected by a massless spring over a pulley on a rough plane with coefficient of friction $\mu$. $A$ force $F$ is applied on block $A$ to the left. Find the minimum value of $M$ to move the block $A$ towards the right.

$A$ uniform wooden stick of mass $1.6 \,kg$ and length $l$ rests in an inclined manner on a smooth, vertical wall of height $h$ < $l$ such that a small portion of the stick extends beyond the wall. The reaction force of the wall on the stick is perpendicular to the stick. The stick makes an angle of $30^{\circ}$ with the wall and the bottom of the stick is on a rough floor. The reaction of the wall on the stick is equal in magnitude to the reaction of the floor on the stick. Find the ratio $h/l$ and the frictional force $f$ at the bottom of the stick. $(g=10 \,m \,s^{-2})$