A block rests on a rough inclined plane making an angle of ${30^o}$ with the horizontal. The coefficient of static friction between the block and the plane is $0.8$. If the frictional force on the block is $10 \,N$, the mass of the block (in kg) is (take $g = 10\,\,m/{s^2})$
AIEEE 2004, Medium
Download our app for free and get started
(a) Angle of repose $\alpha = {\tan ^{ - 1}}(\mu ) = {\tan ^{ - 1}}(0.8) = 38.6^\circ $
Angle of inclined plane is given $\theta = 30^\circ $.
It means block is at rest therefore,
Static friction $=$ component of weight in downward direction $ = mg\sin \theta = 10\;N$
$\therefore m = \frac{{10}}{{9 \times \sin 30^\circ }} = 2\;kg$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1View SolutionThe maximum static frictional force is
- 2A rod $(AB)$ is attached to a fixed point $(C)$ using a light rope $(AC)$. The other end of the rod $(B)$ is sitting on ice with negligible friction and the system is in stationary position. Which of the following can be the equilibrium configuration of this system?View Solution
- 3The coefficient of friction between a body and the surface of an inclined plane at $45^°$ is $0.5.$ If $g = 9.8\,m/{s^2}$, the acceleration of the body downwards in $m/{s^2}$ isView Solution
- 4View SolutionWhich is a suitable method to decrease friction
- 5A block of mass $M = 5\,kg$ is resting on a rough horizontal surface for which the coefficient of friction is $0.2$. When a force $F = 40\,\,N$ is applied, the acceleration of the block will be ........ $m/\sec^2$ $(g = 10\,\,m/{\sec^2})$View Solution
- 6Two blocks $A$ and $B$ of equal masses are sliding down along straight parallel lines on an inclined plane of $45^o$ . Their coefficients of kinetic friction are $\mu _A = 0.2$ and $\mu _B = 0.3$ respectively. At $t = 0$ , both the blocks are at rest and block $A$ is $\sqrt 2$ metre behind block $B$ . The time and distance from the initial position where the front faces of the blocks come in line on the inclined plane as shown in figure. (Use $g = 10\, ms^{-2}$ )View Solution
- 7A $\vec F\,\, = \,\,\hat i\, + \,4\hat j\,$ acts on block shown. The force of friction acting on the block is :View Solution
- 8A disc with a flat small bottom beaker placed on it at a distance $R$ from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity $\omega$. The coefficient of static friction between the bottom of the beaker and the surface of the disc is $\mu$. The beaker will revolve with the disc ifView Solution
- 9A car is moving on a circular path and takes a turn. If ${R_1}$ and ${R_2}$ be the reactions on the inner and outer wheels respectively, thenView Solution
- 10A cylinder of mass $10\,kg$ is sliding on a plane with an initial velocity of $10\,m/s$. If coefficient of friction between surface and cylinder is $ 0.5$, then before stopping it will describe ............. $\mathrm{m}$View Solution