Consider the diagram shown below in which two masses of $m$ and $2m$ are placed on a fixed triangular wedge. The coefficient of friction between block $A$ (mass $m$) and the wedge is $\mu_A = 2/3$,while that for block $B$ (mass $2m$) and the wedge is $\mu_B = 1/3$. Find the acceleration of the system.

Two unequal masses $A$ and $B$ moving along a straight line are brought to rest by equal retarding forces. If $A$ takes double the time taken by $B$ to come to rest and $A$ travels $\frac{2}{3}$ of the distance covered by $B$ before coming to rest,then the ratio of masses of $A$ and $B$ is . . . . . . .

$A$ racing car travels on a track (without banking) $ABCDEFA$. $ABC$ is a circular arc of radius $2R$. $CD$ and $FA$ are straight paths of length $R$ and $DEF$ is a circular arc of radius $R = 100 \, m$. The coefficient of friction on the road is $\mu = 0.1$. The maximum speed of the car on straight paths is $50 \, m/s$. Find the minimum time for completing one round.

$A$ system consists of three masses $m_1, m_2$ and $m_3$ connected by a string passing over a pulley $P$. The mass $m_1$ hangs freely and $m_2$ and $m_3$ are on a rough horizontal table (the coefficient of friction $= \mu$). The pulley is frictionless and of negligible mass. The downward acceleration of mass $m_1$ is (Assume $m_1 = m_2 = m_3 = m$)

$A$ 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

$A$ 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.