Two vertical walls are separated by a distance of 2 m . Wall A is smooth while wall

English

Gujarati

Hindi

6.System of Particles and Rotational Motion

hard

Two vertical walls are separated by a distance of $2\ m$. Wall $A$ is smooth while wall $B$ is rough with a coefficient of friction $0. 5$. A uniform rod is placed between them as shown. The length of longest rod that can be placed between walls is equal to

A

$2\ m$

B

$2\sqrt 2\ m$

C

$\sqrt 5\ m$

D

$\frac{{\sqrt {17} }}{2}\ m$

Solution

$\tau_{\mathrm{com}}=0$

$\mathrm{N} \cdot \frac{\ell}{2} \sin \theta .2=\mu \mathrm{N} \frac{\ell}{2} \cos \theta$

$\Rightarrow \tan \theta=\frac{1}{4}$

$\cos \theta=\frac{2}{\ell}=\frac{-4}{\sqrt{17}}$

$\ell=\frac{\sqrt{17}}{2}$

Standard 11

Physics

Share

Similar Questions

A uniform disc of radius $R$ and mass $M$ is free to rotate only about its axis. A string is wrapped over its rim and a body of mass $m$ is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is

hard

(JEE MAIN-2017)

A solid cylinder of mass $m$ is wrapped with an inextensible light string and, is placed on a rough inclined plane as shown in the figure. The frictional force acting between the cylinder and the inclined plane is:

[The coefficient of static friction, $\mu_{ s },$ is $\left.0.4\right]$

hard

(JEE MAIN-2021)

$A$ sphere is placed rotating with its centre initially at rest ina corner as shown in figure $(a)$ & $(b)$. Coefficient of friction between all surfaces and the sphere is $\frac{1}{3}$. Find the ratio of the frictional force $\frac{{{f_a}}}{{{f_b}}}$ by ground in situations $(a)$ & $(b)$.

normal

$A$ man can move on a horizontal plank supported symmetrically as shown. The variation of normal reaction on support $A$ with distance $x$ of the man from the end of the plank is best represented by :

hard

A uniform beam of weight $W$ is attached to a vertical wall by a hinge $H$ . The beam is held horizontal by a rope as shown below. Which one of the following best shows the direction of the reaction force $R$ at the hinge ?

hard