Laws of Motion Questions

Two masses $m_1=5\text{kg}$ and $m_2=4.8\text{kg}$ tied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when left free to move? (Take $g=9.8{\text{m/s}}^2$)

A block rests on a rough inclined plane making an angle of $30^{\circ }$ with the horizontal. The coefficient of static friction between the block and the plane is $0.8$. If the frictional force on the block is $10\text{N}$, the mass of the block (in kg) is: (take $g=10{\text{m/s}}^2$)

A block of mass $m$ is connected to another block of mass $M$ by a spring (massless) of spring constant $k$. The blocks are kept on a smooth horizontal plane. Initially the blocks are at rest and the spring is unstretched. Then a constant force $F$ starts acting on the block of mass $M$ to pull it. Find the force on the block of mass $m$:

A smooth block is released at rest on a $45^{\circ }$ incline and then slides a distance $d$. The time taken to slide is $n$ times as much to slide on a rough incline than on a smooth incline. The coefficient of friction is:

A block is kept on a frictionless inclined surface with angle of inclination $\alpha$. The incline is given an acceleration $a$ to keep the block stationary. Then $a$ is equal to:

A particle of mass $0.3\text{ kg}$ is subjected to a force $F=-kx$ with $k=15\text{ N/m}$. What will be its initial acceleration if it is released from a point $20\text{ cm}$ away from the origin?

Consider a car moving on a straight road with a speed of $100\text{ m/s}$. The distance at which car can be stopped is [${\mu }_k=0.5$ ]: