The velocity of end A of a rigid rod placed b | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the rod have length $L$. The coordinates of ends $A$ and $B$ are $(0, y)$ and $(x, 0)$ respectively.Since the rod is rigid,$x^2 + y^2 = L^2$.D

Vedclass · Accepted Answer

$u 	an 	heta$

Vedclass · Answer

(B) Let the rod have length $L$. The coordinates of ends $A$ and $B$ are $(0, y)$ and $(x, 0)$ respectively.Since the rod is rigid,$x^2 + y^2 = L^2$.Differentiating with respect to time $t$,we get $2x(dx/dt) + 2y(dy/dt) = 0$.Here,$dy/dt = -u$ (as $y$ is decreasing) and $dx/dt = v$ (velocity of end $B$).So,$xv + y(-u) = 0$,which gives $xv = yu$.From the geometry,$x = L \cos 	heta$ and $y = L \sin 	heta$.Substituting these,$(L \cos 	heta)v = (L \sin 	heta)u$.Therefore,$v = u \frac{\sin 	heta}{\cos 	heta} = u 	an 	heta$.

The velocity of end $A$ of a rigid rod placed between two smooth perpendicular walls moves with velocity $u$ along the vertical direction. Find the velocity of end $B$ of the rod,given that the rod always remains in contact with the walls.

Similar Questions

For the given diagram,when block $B$ is pulled with velocity $V$,the velocity of block $A$ will be:

In the figure shown,the velocities of different blocks are given. The velocity of $C$ is ......... $m/s$.

In the figure shown,the velocity of the lift is $2\,m/s$ upwards. The string is winding on the motor shaft with a velocity of $2\,m/s$ and block $A$ is moving downwards with a velocity of $2\,m/s$ relative to the lift. Find the velocity of block $B$ with respect to the ground.

$A$ rod of length $L$ leans against a smooth vertical wall while its other end is on a smooth floor. The end that leans against the wall moves uniformly vertically downward. Select the correct alternative.

The boxes of masses $2\, {kg}$ and $8\, {kg}$ are connected by a massless string passing over smooth pulleys as shown in the figure. Calculate the time taken by the box of mass $8\, {kg}$ to strike the ground starting from rest. (Use $g = 10\, {m/s^2}$) (in ${s}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module