Given $m_1 = 4m_2$. How much extra distance (in $cm$) does $m_2$ travel before coming to rest?

In a tug-of-war contest,two men pull on a horizontal rope from opposite sides. The winner will be the man who

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 ...........

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

$A$ 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?

One end of a spring of force constant $150 \text{ dyne cm}^{-1}$ is connected to a block of mass $0.2 \text{ kg}$ kept on a rough horizontal surface of coefficient of friction $0.3$. The other end of the spring is connected to a rigid support as shown in the figure and the spring is initially undeformed. The maximum velocity $v$ that can be given to the block so that it travels only in one direction is . . . . . . $\text{ms}^{-1}$. (Acceleration due to gravity $= 10 \text{ ms}^{-2}$)