$A$ particle of mass $m$ is acted upon by a force $F$ given by the empirical law $F = \frac{R}{t^2} v(t)$. If this law is to be tested experimentally by observing the motion starting from rest,the best way is to plot:

Two beads connected by a massless inextensible string are placed over a fixed ring as shown in the figure. The mass of each bead is $m$,and there is no friction between bead $B$ and the ring. Find the minimum value of the coefficient of friction between bead $A$ and the ring so that the system remains in equilibrium. ($C$ is the center of the ring,and the line $AC$ is vertical.)

$A$ block of mass $M = 10\,kg$ rests on a horizontal table. The coefficient of friction between the block and the table is $\mu = 0.05.$ When hit by a bullet of mass $m = 50\,g$ moving with speed $v,$ which gets embedded in it,the block moves and comes to a stop after moving a distance of $2\,m$ on the table. If a freely falling object were to acquire speed $\frac{v}{10}$ after being dropped from height $H,$ then neglecting energy losses and taking $g = 10\,m/s^2,$ the value of $H$ is close to ................. $km$.

$A$ particle initially at rest is subjected to two forces. One is constant,the other is a retarding force proportional to the particle velocity. In the subsequent motion of the particle,

What is the relationship between $W_1$ and $W_2$?

Two situations are shown in figures $(a)$ and $(b)$. In each case,$m_1 = 3 \ kg$ and $m_2 = 4 \ kg$. If $a_1$ and $a_2$ are the respective accelerations of the blocks in these situations,then the values of $a_1$ and $a_2$ are respectively [ $g = 10 \ ms^{-2}$ ]