$A$ block of mass $m$ is pressed against a vertical wall by a horizontal force of magnitude $mg$. An upward force of magnitude $\frac{mg}{2}$ is also applied to the block. If the block is in equilibrium,the minimum coefficient of friction $\mu$ between the block and the wall is:

Two masses $m_1 = 10 \text{ kg}$ and $m_2 = 20 \text{ kg}$ are connected by an inextensible string over a frictionless pulley,as shown in the figure. The coefficient of friction of the horizontal surface is $\mu = 0.15$. The minimum mass $m$ that should be placed on top of $m_2$ to stop the motion is:

$A$ heavy box is pushed across a rough floor with an initial speed of $4 \, m/s$. It stops moving after $8 \, s$. If the average resisting force of friction is $10 \, N$,the mass of the box (in $kg$) is:

$A$ $2 \, kg$ block on ice is given a velocity of $6 \, m/s$. If it comes to rest in $10 \, s$,what is the coefficient of friction?

When we rub our palms,they get heated,but only up to a maximum temperature because:

$A$ boat of mass $700 \,kg$ is travelling at a speed of $24 \,ms^{-1}$ when its engine is shut off. The magnitude of frictional force $f$ between the boat and water is given by $f = 35v$, where $v$ is the speed in $ms^{-1}$ and $f$ is in newton. Find the time taken for the speed of the boat to become $6 \,ms^{-1}$. (in $\,s$)