An engine of mass $1$ metric ton is ascending an inclined plane,at an angle $\theta = \tan^{-1}(1/2)$ with the horizontal,with a speed of $36 \; km/h$. If the coefficient of friction of the surface is $1/\sqrt{3}$,then the power developed by the engine is:

The upper half of an inclined plane of inclination $\theta$ is perfectly smooth,while the lower half is rough. $A$ body starting from rest at the top comes back to rest at the bottom. The coefficient of friction $\mu$ for the lower half is given by:

Consider a uniform cubical box of side $a$ on a rough floor that is to be moved by applying a minimum possible force $F$ at a point $b$ above its centre of mass (see figure). If the coefficient of friction is $\mu = 0.4$,the maximum possible value of $100 \times \frac{b}{a}$ for a box not to topple before moving is

$A$ force of $750 \, N$ is applied to a block of mass $102 \, kg$ to prevent it from sliding on a plane with an inclination angle $30^{\circ}$ with the horizontal. If the coefficients of static friction and kinetic friction between the block and the plane are $0.4$ and $0.3$ respectively,then the frictional force acting on the block is...... $N$.

$A$ block of mass $5 \text{ kg}$ starts up a $45^{\circ}$ inclined plane with an initial kinetic energy of $100 \text{ J}$. If the coefficient of friction between the block and the plane is $0.5$,then the distance covered by the block before it stops is (Acceleration due to gravity $= 10 \text{ ms}^{-2}$)

$A$ uniform chain of length $L$ hangs partly from a table and is kept in equilibrium by friction. If the maximum length that can hang without slipping is $\ell$,then the coefficient of friction between the table and the chain is: