A uniform rod of length $l$ is being rotated in a horizontal plane with a constant angular speed about an axis passing through one of its ends. If the tension generated in the rod due to rotation is $T(x)$ at a distance $x$ from the axis, then which of the following graphs depicts it most closely?
JEE MAIN 2019, Difficult
Download our app for free and get started
$T = \int_{x - x}^{x - \ell } {dm{\omega ^2}x = \int_{x - x}^{x - \ell } {\frac{m}{\ell }dx{\omega ^2}x\,T} } $
$ = \frac{{m{\omega ^2}}}{{2\ell }}\left( {{\ell ^2} - {x^2}} \right)$
$T = \frac{{m{\omega ^2}}}{{2\ell }}\left( {{\ell ^2} - {x^2}} \right)$
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
- 1A block of mass $5\,kg$ is placed at rest on a table of rough surface. Now, if a force of $30\,N$ is applied in the direction parallel to surface of the table, the block slides through a distance of $50\,m$ in an interval of time $10\,s$. Coefficient of kinetic friction is (given, $g =10\,ms ^{-2}$)View Solution
- 2The coefficient of static friction between a wooden block of mass $0.5\, kg$ and a vertical rough wall is $0.2$ The magnitude of horizontal force that should be applied on the block to keep it adhere to the wall will be $N$ $\left[ g =10\, ms ^{-2}\right]$View Solution
- 3View SolutionIf the overbridge is concave instead of being convex, the thrust on the road at the lowest position will be
- 4A block of mass $40 \,kg$ slides over a surface, when a mass of $4 \,kg$ is suspended through an inextensible massless string passing over frictionless pulley as shown below. The coefficient of kinetic friction between the surface and block is $0.02$. The acceleration of block is ............ $ms ^{-2}$ (Given $g =10 \,ms ^{-2}$.)View Solution
- 5View SolutionA metal block is resting on a rough wooden surface. A horizontal force applied to the block is increased uniformly. Which of the following curves correctly represents velocity of the block ?
- 6If 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 isView Solution
- 7A 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
- 8In the figure shown, horizontal force $F_1$ is applied on a block but the block does not slide. Then as the magnitude of vertical force $F_2$ is increased from zero the block begins to slide; the correct statement isView Solution
- 9A conveyor belt is moving at a constant speed of $2\, m s^{-1}$. A box is gently dropped on it. The coefficient of friction between them is $\mu = 0.5.$ The distance that the box will move relative to belt before coming to rest on it, taking $g = 10\, m s^{-2},$ is ........... $m$View Solution
- 10In the diagram, $BAC$ is a rigid fixed rough wire and angle $BAC$ is $60^o$. $P$ and $Q$ are two identical rings of mass $m$ connected by a light elastic string of natural length $2a$ and elastic constant $\frac{mg}{a}$. If $P$ and $Q$ are in equilibrium when $PA = AQ = 3a$ then the least coefficient of friction between the ring and the wire is $\mu$. Then value of $\mu + \sqrt 3 $ is :-View Solution
