The figure shows an iron slab of mass 4.0 kg attached to a box having a mass of 5.0 kg via a massless string. The pulley connecting them has a mass of 150 g and a radius of 10 cm. Calculate the magnitude of acceleration experienced by the iron slab if it has a force of 25 N applied toward the left. Also, calculate the magnitude of tension(s) in different parts of the string. Consider the pulley and the horizontal surface to be frictionless.

Consider an arrangement of massless and frictionless pulleys used to connect a bag weighing 4.0 kg to a block of 1.5 kg through a massless string as shown in the figure. Determine the magnitude of the acceleration of the 1.5 kg block.

A 2.0 kg book is on top of a 3.0 kg book placed on the floor. If the acceleration of the 3.0 kg book is a = 1.2 m/s², what is the required minimum coefficient of friction μ between the books for the book on top to not slide off? (Assume μ = μ_s = μ_k)

As shown in the figure, a block of mass 2.0 kg is attached to another block weighing 750 g through a massless string. The coefficients of static and dynamic friction between the block and incline are 0.45 and 0.25 respectively. The block on the inclined surface is pulled up to the top of the plane. At this point determine whether the block will remain steady or move downwards on the inclined plane.

A wooden block (block W) and a metallic block (block M) are tied together by a lightweight cord and slide down an inclined plane at an angle $\theta=30^{\circ}$ to the horizontal. The masses of the blocks are $m_W=m_M=5.0\ kg$. The coefficients of friction for the wooden and metallic blocks are $\mu_{W}=0.25$ and $\mu_{M}=0.35$, respectively. Calculate the acceleration of the system as the blocks slide down the incline.

A worker pulls two crates, A and B, along a horizontal surface with a rope that is attached to both crates. The coefficient of friction between the crates and the surface is 0.15. If the tension in the rope between crate B and the worker is 200 N, what is the tension in the rope between crate A and crate B ? Consider that crate A has a mass of 20 kg and crate B has a mass of 15 kg. Both crates are being pulled with a constant acceleration of 2.5 m/s². Assume that the rope is massless and there is no slippage between the crates and the surface.

A boy named Kevin having a mass of 65 kg starts riding a bicycle on a flat road. The bicycle has a force of 125 N pushing it forward and a coefficient of kinetic friction on the road of 0.18. The chain on the bicycle falls off after 25 s. Determine the top speed attained by Kevin.

As shown in the figure, a force of 15 N is acting on a 2.5 kg steel box against a vertically lubricated steel surface. Determine whether the block will move vertically up or down or remain at its place if it is initially at rest.

A 3.5 kg block when placed on a spring compresses it to 25 cm. The spring is 33 cm long and is placed vertically with one end fixed on the ground. Determine the spring constant.

An ideal spring is welded at one end to the smooth surface of a spin coater. The spring rests horizontally on the surface and has an equilibrium length of 14 cm. A small object of mass 55 g is fixed to the free end. The spin coater is rotated at a speed of 125 rpm. Once the object moves in a circular path at a constant speed, the spring length becomes 18 cm. Calculate the spring constant.