A particle is projected with a speed ${v_0} = \sqrt {gR} $ . The coefficient of friction between the particle and the hemispherical plane is $\mu  = 0.5$ . Then, the initial acceleration of the particle is

$STATEMENT-1$ It is easier to pull a heavy object than to push it on a level ground. and

$STATEMENT-2$ The magnitude of frictional force depends on the nature of the two surfaces in contact.

What is the acceleration of the block and trolley system shown in a Figure, if the coefficient of kinetic friction between the trolley and the surface is $0.04$? What is the tension in the string ? (Take $g = 10\; m s^{-2}$). Neglect the mass of the string.

Which of the following is a self adjusting force?

A block of mass $4\, kg$ rests on an inclined plane. The inclination of the plane is gradually increased. it is found that when the inclination is $3$ in $5\left( {\sin \theta  = \frac{3}{5}} \right)$, the block just begins to slide down the plane. The coefficient of friction between the block and the plane is

A uniform wooden stick of mass $1.6 \mathrm{~kg}$ and length $l$ rests in an inclined manner on a smooth, vertical wall of height $h( < l)$ such that a small portion of the stick extends beyond the wall. The reaction force of the wall on the stick is perpendicular to the stick. The stick makes an angle of $30^{\circ}$ with the wall and the bottom of the stick is on a rough focr. The reaction of the wall on the stick is equal in magnitude to the reaction of the floor on the st $ck$. The ratio $h / l$ and the frictional force $f$ at the bottom of the stick are $\left(g=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$