A road is $10\, m$ wide. Its radius of curvature is $50\, m$. The outer edge is above the lower edge by a distance of $1.5\, m$. This road is most suited for the velocity .......... $m/\sec$
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An insect crawls up a hemispherical surface very slowly. The coefficient of friction between the insect and the surface is $1/3$. If the line joining the centre of the hemispherical surface to the insect makes an angle $\alpha $ with the vertical, the maximum possible value of $\alpha $ so that the insect does not slip is given by
The coefficient of static friction, ${\mu _s},$ between block $A$ of mass $2\, kg$ and the table as shown in the figure is $0.2$. ........ $kg$ would be the maximum mass value of block $B$ so that the two blocks do not move. The string and the pulley are assumed to be smooth and massless. $(g = 10\,m/{s^2})$
A uniform rope of total length $l$ is at rest on a table with fraction $f$ of its length hanging (see figure). If the coefficient of friction between the table and the chain is $\mu$, then
Shown in the diagram is a system of two bodies, a block of mass $m$ and a disc of mass $4\ m$ , held in equilibrium. If the string $3$ is burnt, find the acceleration of the disc. Neglect the masses of the pulleys $P$ and $Q$ . The co-efficient of friction between the block and horizontal surface is $0.5$ and friction between disc and string is zero ........ $m/s^2$
A steel block of $10\, {kg}$ rests on a horizontal floor as shown. When three iron cylinders are placed on it as shown, the block and cylinders go down with an acceleration $0.2\, {m} / {s}^{2}$. The normal reaction ${R}$ by the floor if mass of the iron cylinders are equal and of $20\, {kg}$ each, is .....$N.$ [Take ${g}=10\, {m} / {s}^{2}$ and $\mu_{{s}}=0.2$ ]
A block is placed on a rough horizontal plane. A time dependent horizontal force $F = Kt$ acts on the block. Here $K$ is a positive constant. Acceleration-time graph of the block is