A block is projected with speed $20 \,m / s$ on a rough horizontal surface. The coefficient of friction $(\mu)$ between the surfaces varies with time $(t)$ as shown in figure. The speed of body at the end of $4$ second will be ............ $m / s$ ( $g=$ $10 \,m / s ^2$ )
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A particle of mass $m$ is at rest at the origin at time $t = 0$. It is subjected to a force $F(t) = F_0e^{-bt}$ in the $x$ -direction. Its speed $v(t)$ is depicted by which of the following curves ?
A uniform rope of length l lies on a table. If the coefficient of friction is $\mu $, then the maximum length ${l_1}$ of the part of this rope which can overhang from the edge of the table without sliding down is
A block of mass $M$ slides down on a rough inclined plane with constant velocity. The angle made by the incline plane with horizontal is $\theta$. The magnitude of the contact force will be.
A body takes just twice the time as long to slide down a plane inclined at $30^o$ to the horizontal as if the plane were frictionless. The coefficient of friction between the body and the plane is
A body of weight $64\, N$ is pushed with just enough force to start it moving across a horizontal floor and the same force continues to act afterwards. If the coefficients of static and dynamic friction are $0.6$ and $0.4$ respectively, the acceleration of the body will be (Acceleration due to gravity $= g$)
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 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
Block $A$ of mass $m$ and block $B$ of mass $M$ are connected by a massless spring over a pulley on a rough plane with coefficient of friction as $μ$. A force $F$ is applied on block $A$ to the left. Find the minimum value of $M$ to move the block $A$ towards right