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Two blocks $A$ and $B$ of masses $6\, kg$ and $3\, kg$ rest on a smooth horizontal surface as shown in the figure. If coefficient of friction between $A$ and $B$ is $0.4$, the maximum horizontal force which can make them without separation is ........ $N$
A block is lying on an inclined plane which makes $60^°$ with the horizontal. If coefficient of friction between block and plane is $0.25$ and $g = 10\,m/{s^2}$, then acceleration of the block when it moves along the plane will be ........ $m/s^2$
A uniform chain is at rest partially on the incline and partially hanging vertically. Coefficient of friction between chain and incline is $\mu = \frac{1}{{2\sqrt 3 }}$. The ratio of $\frac{{{L_{\max }}}}{{{L_{\min }}}}$ is $(L_{max} =$ maximum length of chain kept on inclined so that chain remains at rest, $L_{min} =$ minimum length of chain kept on incline so that chain remains at rest)
A circular road of radius $1000 \,m$ has banking angle ${45^o}$. The maximum safe speed of a car having mass $2000 \,kg$ will be, if the coefficient of friction between tyre and road is $0.5$ ....... $m/s$
Put a uniform meter scale horizontally on your extended index fingers with the left one at $0.00 cm$ and the right one at $90.00 cm$. When you attempt to move both the fingers slowly towards the center, initially only the left finger slips with respect to the scale and the right finger does not. After some distance, the left finger stops and the right one starts slipping. Then the right finger stops at a distance $x_R$ from the center ( $50.00 cm$ ) of the scale and the left one starts slipping again. This happens because of the difference in the frictional forces on the two fingers. If the coefficients of static and dynamic friction between the fingers and the scale are $0.40$ and $0.32$ , respectively, the value of $x_R($ in $cm )$ is. . . . . . .
Calculate the acceleration (In $m/s^{2}$) of the block and trolly system shown in the figure. The coefficient of kinetic friction between the trolly and the surface is $0.05 .\left( g =10\; m / s ^{2},\right.$ mass of the string is negligible and no other friction exists).
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 $\left(g=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$