$A$ 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 $10N/kg.$
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An inclined plane is bent in such a way that the vertical cross-section is given by $y =\frac{ x ^{2}}{4}$ where $y$ is in vertical and $x$ in horizontal direction. If the upper surface of this curved plane is rough with coefficient of friction $\mu=0.5,$ the maximum height in $cm$ at which a stationary block will not slip downward is............$cm$
A cube of mass $m$ slides down an inclined right-angle trough. If the coefficient of kinetic friction between the cube and the trough is $\mu _k$ , then the acceleration of the block is
On a rough horizontal surface, a body of mass $2 \,kg$ is given a velocity of $10 \,m/s$. If the coefficient of friction is $0.2$ and $g = 10\, m/{s^2}$, the body will stop after covering a distance of ........ $m$
A disc rotates about its axis of symmetry in a hoizontal plane at a steady rate of $3.5$ revolutions per second. A coin placed at a distance of $1.25\,cm$ from the axis of rotation remains at rest on the disc. The coefficient of friction between the coin and the disc is $(g\, = 10\,m/s^2)$
A ball of mass $0.1\, Kg$. is whirled in a horizontal circle of radius $1\, m$. by means of a string at an initial speed of $10\, R.P.M.$ Keeping the radius constant, the tension in the string is reduced to one quarter of its initial value. The new speed is ....... $r.p.m.$
A hollow vertical cylinder of radius $R$ is rotated with angular velocity $\omega$ about an axis through its center. What is the minimum coefficient of static friction necessary to keep the mass $M$ suspended on the inside of the cylinder as it rotates?
Two masses $A$ and $B$ of $10\, kg$ and $5 \,kg$ respectively are connected with a string passing over a frictionless pulley fixed at the corner of a table as shown. The coefficient of static friction of $A$ with table is $0.2$. The minimum mass of $C$ that may be placed on $A$ to prevent it from moving is ........ $kg$
A block of $200\, g$ mass moves with a uniform speed in a horizontal circular groove, with vertical side walls of radius $20\, cm$. If the block takes $40\, s$ to complete one round, the normal force by the side walls of the groove is
If the coefficient of friction between block & wedge is $\mu $, then the maximum horizontal acceleration of the wedge for which block will remain at rest w.r.t. the wedge is
In a conical pendulum, the bob is rotated with different angular velocities and tension in the string is calculated for different values of $\omega$ . Which of them is correct graph between $T$ & $\omega .$