A block of mass $m$ is on an inclined plane of angle $\theta$. The coefficient of friction between the block and the plane is $\mu$ and $\tan \theta>\mu$. The block is held stationary by applying a force $\mathrm{P}$ parallel to the plane. The direction of force pointing up the plane is taken to be positive. As $\mathrm{P}$ is varied from $\mathrm{P}_1=$ $m g(\sin \theta-\mu \cos \theta)$ to $P_2=m g(\sin \theta+\mu \cos \theta)$, the frictional force $f$ versus $P$ graph will look like

  • [IIT 2010]
  • A
    223245-a
  • B
    223245-b
  • C
    223245-c
  • D
    223245-d

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A block of mass $0.1 \,kg$ is held against a wall by applying a horizontal force of $5\, N$ on the block. If the coefficient of friction between the block and the wall is $0.5$, the magnitude of the frictional force acting on the block is ........ $N$

  • [IIT 1994]

A circular racetrack of radius $300\; m$ is banked at an angle of $15^o$. If the coefficient of friction between the wheels of a race-car and the road is $0.2$, what is the

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In the figure, a ladder of mass $m$ is shown leaning against a wall. It is in static equilibrium making an angle $\theta$ with the horizontal floor. The coefficient of friction between the wall and the ladder is $\mu_1$ and that between the floor and the ladder is $\mu_2$. The normal reaction of the wall on the ladder is $N_1$ and that of the floor is $N_2$. If the ladder is about to slip, then

$Image$

$(A)$ $\mu_1=0 \mu_2 \neq 0$ and $N _2 \tan \theta=\frac{ mg }{2}$

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  • [IIT 2014]

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 ?

If mass of $A = 10\,\,kg$, coefficient of static friction $= 0.2$, coefficient of kinetic friction = $0.2$. Then mass of $B$ to start motion is