$A$ block of mass $M$ is placed on $a$ horizontal surface and it is tied with an inextensible string to $a$ block of mass, as shown in figure. A block of mass $m_0$ is also placed on $M$ The minimum value of $\mu$ between the block $M$ and $m_0$ (taking horizontal surface frictionless) for which all the three blocks move together, is
Difficult
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A $60\, kg$ body is pushed with just enough force to start it moving across a floor and the same force continues to act afterwards. The coefficient of static friction and sliding friction are $0.5$ and $0.4$ respectively. The acceleration of the body is ........ $m/{s^2}$
In the arrangement shown in the figure, mass of the block $B$ and $A$ is $2m$ and $m$ respectively. Surface between $B$ and floor is smooth. The block $B$ is connected to the block $C$ by means of a string pulley system. If the whole system is released, then find the minimum value of mass of block $C$ so that block $A$ remains stationary $w.r.t. B$. Coefficient of friction between $A$ and $B$ is $\mu$
$Assertion$ : Angle of repose is equal to the angle of limiting friction.
$Reason$ : When the body is just at the point of motion, the force of friction in this stage is called limiting friction.
A block of mass $M$ is sliding down the plane. Coefficient of static friction is $\mu _s$ and kinetic friction is $\mu _k.$ Then friction force acting on the block 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 $30°$ 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...... $N$
$A$ long plank $P$ of the mass $5\, kg$ is placed on a smooth floor. On $P$ is placed a block $Q$ of mass $2\, kg$. The coefficient of friction between $P$ and $Q$ is $0.5$. If a horizontal force $15N$ is applied to $Q$, as shown, and you may take $g$ as $10N/kg.$
A particle is describing circular motion in a horizontal plane in contact with the smooth inside surface of a fixed right circular cone with its axis vertical and vertex down. The height of the plane of motion above the vertex is $h$ and the semivertical angle of the cone is $\alpha $ . The period of revolution of the particle
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 $\mu_{{s}}=0.2$ ]
The coefficient of static friction between two blocks is $0.5$ and the table is smooth. The maximum horizontal force that can be applied to move the blocks together is $\ldots \ldots . N$. (take $\left.g=10\, {ms}^{-2}\right)$
A block of mass $m$ is placed on a surface with a vertical coss section given by $y = \frac{{{x^3}}}{6}$ . If the coefficient of friction is $0.5$, the maximum height above the ground at which the block can be placed without slipping is