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.

An ideal spring is connected between two blocks of masses $M$ and $m$. This system can move on a smooth horizontal table. The blocks are brought closer to compress the spring and then released. In the subsequent motion,select the true statement$(s)$:
$(a)$ They move in opposite directions with speeds inversely proportional to their masses.
$(b)$ The ratio of their speeds remains constant.
$(c)$ Linear momentum and energy of the system remain conserved.

$A$ $1\; kg$ block situated on a rough incline is connected to a spring of spring constant $100\; N m^{-1}$ as shown in the figure. The block is released from rest with the spring in the unstretched position. The block moves $10\; cm$ down the incline before coming to rest. Find the coefficient of friction between the block and the incline. Assume that the spring has a negligible mass and the pulley is frictionless.

$A$ man is standing on a spring platform. The reading of the spring balance is $60\, kg$ wt. If the man jumps off the platform,what happens to the reading of the spring balance?

$A$ cylinder is placed on a rough plank,which in turn is placed on a smooth surface. The plank is pulled with a constant force $F$. Indicate the correct direction of the friction force acting on the cylinder.

$A$ truck of mass $2800 \ kg$ is moving at a speed of $15 \ m/s$. $A$ frictional force of $500 \ N$ and a forward force of $1200 \ N$ act on it. The distance covered by the truck in $10 \ s$ is .......... $m$.