In the figure,a block of weight $60 \, N$ is placed on a rough surface. The coefficient of friction between the block and the surface is $0.5$. Find the maximum weight $W$ such that the block does not slip on the surface.

$A$ 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. Find the downward acceleration of mass $m_1$. (Assume $m_1 = m_2 = m_3 = m$)

What is the acceleration of the block and trolley system shown in the figure,if the coefficient of kinetic friction between the trolley and the surface is $0.04$? What is the tension in the string? (Take $g = 10\; m s^{-2}$). Neglect the mass of the string.

Two blocks of equal masses are connected with a massless spring of spring constant $k = 2500 \,N/m$ and natural length $10 \,cm$,resting on a frictionless horizontal plane. If a constant horizontal force $F = 10 \,N$ is applied as shown in the figure,find the maximum distance between the blocks. (in $cm$)

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 . . . . . . .

$A$ bullet of mass $0.1\, kg$ is fired into a wooden block to pierce through it,but it stops after moving a distance of $50\, cm$ into it. If the velocity of the bullet before hitting the wood is $10\, m/s$ and it slows down with uniform deceleration,then the magnitude of the effective retarding force on the bullet is $'x'\, N$. The value of $'x'$ to the nearest integer is: