Exercise - 1

Two blocks $m_1=4 \mathrm{kg}$ and $m_2=2 \mathrm{kg}$, connected by a weightless rod on a plane having inclination of $37°$ as shown in the figure. The coefficients of dynamic friction of $m_1$ and $m_2$ with the inclined plane is $\mathrm{\mu }=0.25$. Then the common acceleration of the two blocks and the tension in the rod are: (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

If the normal force is doubled, the coefficient of friction is:

A cart of mass $M$ has a block of mass $m$ attached to it as shown in the figure. Co-efficient of friction between the block and cart is $\mu$. What is the minimum acceleration of the cart so that the block m does not fall?

A block of mass $1\text{ kg}$ lies on a horizontal surface in a truck. The coefficient of static friction between the block and the surface is $0.6$. If the acceleration of the truck is $5 {\text{m s}}^{-2}$, the frictional force acting on the block is:

Two masses $A$ and $B$ of $10 \mathrm{kg}$ and $5 \mathrm{kg}$ respectively are connected with a string passing over a frictionless pulley fixed at the corner of a table as shown. The coefficient of static friction of $A$ with table is $0.2$. The minimum mass of $C$ that may be placed on $A$ to prevent it from moving is

A $60 \mathrm{kg}$ body is pushed horizontally with just enough force to start it moving across a floor and the same force continues to act afterwards. The coefficient of static friction and sliding friction are $0.5$ and $0.4$ respectively. The acceleration of the body is:

A force $F=t$ is applied to block $A$ as shown in the figure. The force is applied at $t=0 \mathrm{s}$ when the system was at rest and the string is just straight without tension. Which of the following graphs gives the friction force between $B$ and horizontal surface as a function of time $t$?

A man of mass $m$ is applying a horizontal force to slide a box of mass $m\text{'}$ on a rough horizontal surface. It is known that the man does not slide. The coefficient of friction between the shoes of the man and the floor is $\mathrm{\mu }$ and between the box and the floor is $\mathrm{\mu }\text{'}$. In which of the following cases it is certainly not possible to slide the box?