$A$ 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 $M$ If $\mu < \mu_{min}$ (the minimum friction required to keep the block $m$ stationary), then the downward acceleration of $m$ is
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A chain of length $L$ rests on a rough table. If $\mu $ be the coefficient of friction, the maximum friction of the chain that can hang over the table will be
A horizontal force of $10 \,N$ is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is $0.2$. the weight of the block is ........ $N$
Imagine the situation in which the given arrangement is placed inside a trolley that can move only in the horizontal direction, as shown in figure. If the trolley is accelerated horizontally along the positive $x$ -axis with $a_0$, then Identify the correct statement $(s)$ related to the tension $T$ in the string
A $2 \,kg$ mass starts from rest on an inclined smooth surface with inclination $30^°$ and length $2\, m$. ...... $m$ will it travel before coming to rest on a frictional surface with frictional coefficient of $0.25$
Two masses $M$ and $m$ are attached to a vertical axis by weightless threads of combined length $l$. They are set in rotational motion in a horizontal plane about this axis with constant angular velocity $\omega $. If the tensions in the threads are the same during motion, the distance of $M$ from the axis is
A rocket is fired vertically frorn the earth with an acceleration of $2\,g,$ where $g$ is the gravitational acceleration. On an inclined plane inside the rocket, making an angle $\theta $ with the horizontal, a point object of mass $m$ is kept. The minimum coefficient of friction $\mu _{min}$ between the mass and the inclined surface such that the mass does not move is
A roller coaster is designed such that riders experience "weightlessness" as they go round the top of a hill whose radius of curvature is $20\, m.$ The speed of the car at the top of the hill is between