A block of mass $m$ lying on a rough horizontal plane is acted upon by a horizontal force $P$ and another force $Q$ inclined at an angle $\theta $ to the vertical. The block will remain in equilibrium, if the coefficient of friction between it and the surface is
Difficult
Download our app for free and get started
(a) By drawing the free body diagram of the block for critical condition
$F = \mu \,R$ $⇒$ $P + Q\sin \theta $
$ = \mu \,(mg + Q\cos \theta )$
$\therefore \mu = \frac{{P + Q\sin \theta }}{{mg + Q\cos \theta }}$
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
- 1As shown in the figure, two strings of length $l$ each are attached with a vertical axis $AB$ of length $l$. Strings are $AC$ and $BC$. At point $C$ a point mass m is attached. Mass rotates about axis with angular velocity. Tensions in $AB$ and $BC$ are $T_1$ and $T_2$ respectively. Choose the $CORRECT$ alternative :-View Solution
- 2In 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 $T$ & $\omega .$View Solution
- 3A block of mass $m$ is placed on a surface with a vertical coss section given by $y = \frac{{{x^3}}}{6}$ . If the coefficient of friction is $0.5$, the maximum height above the ground at which the block can be placed without slipping isView Solution
- 4A force $F = Kt$ (where $t$ is the time in seconds and $K = 2\, N/s$) is applied on $2 \,kg$ block at $t = 0$ as shown in the figure. The displacement of $8\ kg$ block till the time when $2\, kg$ block start slipping on $8\,kg$ block will be (coefficient of friction between $2\,kg$ block and $8\, kg$ block is $0.2$ and between $8\, kg$ block and surface is zero,View Solution
$g = 10m/s^2)$
- 5A bullet of mass $4\,g$ is fired horizontally with a speed of $300\,m/s$ into $0.8\,kg$ block of wood at rest on a table. If the coefficient of friction between the block and the table is $0.3,$ how far will the block slide approximately?View Solution
- 6A force of $19.6\, N$ when applied parallel to the surface just moves a body of mass $10 \,kg$ kept on a horizontal surface. If a $5\, kg$ mass is kept on the first mass, the force applied parallel to the surface to just move the combined body is........ $N.$View Solution
- 7A block of mass $1 \,kg$ is projected from the lowest point up along the inclined plane. If $g=10 \,ms ^{-2}$, the retardation experienced by the block is ............. $ms ^ {-2}$View Solution
- 8In figure, the coefficient of friction between the floor and the block $B$ is $0.1$. The coefficient of friction between the blocks $B$ and $A$ is $0.2$. The mass of $A$ is $\frac{m}{2}$ and of $B$ is $m$. ........ $mg$ is the maximum horizontal force $F$ can be applied to the block $B$ so that two blocks move together ?View Solution
- 9A uniform rope of total length $l$ is at rest on a table with fraction $f$ of its length hanging (see figure). If the coefficient of friction between the table and the chain is $\mu$, thenView Solution
- 10A uniform chain of $6\, m$ length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The co-efficient of static friction between the chain and the surface of the table is $0.5$, the maximum length of the chain hanging from the table is.......$m.$View Solution