In the given arrangement of a doubly inclined plane two blocks of masses $\mathrm{M}$ and $\mathrm{m}$ are placed. The blocks are connected by a light string passing over an ideal pulley as shown. The coefficient of friction between the surface of the plane and the blocks is $0.25$ . The value of $\mathrm{m}$, for which $\mathrm{M}=10$ $\mathrm{kg}$ will move down with an acceleration of $2 \mathrm{~m} / \mathrm{s}^2$, is : (take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ and $\left.\tan 37^{\circ}=3 / 4\right)$
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A block of mass $5$ kg lies on a rough horizontal table. A force of $19.6\, N$ is enough to keep the body sliding at uniform velocity. The coefficient of sliding friction is
A block of mass $5\, kg$ is $(i)$ pushed in case $(A)$ and $(ii)$ pulled in case $(B)$, by a force $F = 20\, N$, making an angle of $30^o$ with the horizontal, as shown in the figures. The coefficient of friction between the block and floor is $\mu = 0.2$. The difference between the accelerations of the block, in case $(B)$ and case $(A)$ will be ........ $ms^{-2}$ .$(g = 10\, ms^{-2})$
A block of mass $m$ lying on a rough horizontal plane is acted upon by a horizontal force $P$ and another force $Q$ inclined at an angle $\theta $ to the vertical. The block will remain in equilibrium, if the coefficient of friction between it and the surface is
A solid hemisphere of weight $P$ rests with its curved surface in contact with a rough inclined plane. A weight $Q$ is placed at some point on the rim of the hemisphere to keep its plane surface horizontal then its minimum coefficient of friction is
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 uniform metal chain is placed on a rough table such that one end of chain hangs down over the edge of the table. When one-third of its length hangs over the edge, the chain starts sliding. Then, the coefficient of static friction is
A heavy uniform chain lies on a horizontal table-top. If the coefficient of friction between the chain and table surface is $0.25$, then the maximum fraction of length of the chain, that can hang over one edge of the table is ...... $\%$
A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force $2\,N$ down the inclined plane. The maximum external force up the inclined plane that does not move the block is $10\,N.$ The coefficient of static friction between the block and the plane is : [Take $g = 10\,m/s^2$ ]
Two blocks $A$ and $B$ of masses $m_A = 1\,kg$ and $m_B = 3\,kg$ are kept on the table as shown in figure. The coefficient of friction between $A$ and $B$ is $0.2$ and between $B$ and the surface of the table is also $0.2.$ The maximum force $F$ that can be applied on $B$ horizontal, so that the block $A$ does not slide over the block $B$ is $...... N. [$Take $g = 10\,m/s^2 ]$