For the given diagram,when block B is pulled | vedclass

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

Question

(C) Let the length of the string be $L$. Let $x_A$ and $x_B$ be the horizontal distances of blocks $A$ and $B$ from the vertical line passing through

Vedclass · Accepted Answer

$V \sqrt{3}$

Vedclass · Answer

(C) Let the length of the string be $L$. Let $x_A$ and $x_B$ be the horizontal distances of blocks $A$ and $B$ from the vertical line passing through the pulley,and $h$ be the height of the pulley from the ground.The length of the string is $L = \sqrt{x_A^2 + h^2} + \sqrt{x_B^2 + h^2}$.Differentiating with respect to time $t$,we get $0 = \frac{x_A}{\sqrt{x_A^2 + h^2}} \frac{dx_A}{dt} + \frac{x_B}{\sqrt{x_B^2 + h^2}} \frac{dx_B}{dt}$.Since $\cos 	heta = \frac{x}{\sqrt{x^2 + h^2}}$,we have $v_A \cos 	heta_A + v_B \cos 	heta_B = 0$ (considering components along the string).Here,the velocity of the string along the segment connected to $B$ is $v_B \cos(30^\circ) = V \cos(30^\circ)$.The velocity of the string along the segment connected to $A$ is $v_A \cos(60^\circ)$.Since the string is inextensible,the velocity component along the string must be equal for both sides: $v_A \cos(60^\circ) = V \cos(30^\circ)$.$v_A (1/2) = V (\sqrt{3}/2)$.$v_A = V \sqrt{3}$.

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

Similar Questions

What is the acceleration of block $B$ for the given system?

$A$ block is dragged on a smooth plane with the help of a rope which moves with a velocity $v$ as shown in the figure. The horizontal velocity of the block is

In the arrangement shown in the figure,the block of mass $m=2\,kg$ lies on the wedge of mass $M=8\,kg$. Find the initial acceleration of the wedge if the surfaces are smooth and the pulley and strings are massless.

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.

$A$ block $Q$ of mass $M$ is placed on a horizontal frictionless surface $AB$ and a body $P$ of mass $m$ is released on its frictionless slope. As $P$ slides by a length $L$ on this slope of inclination $\theta$,the block $Q$ would slide by a distance:

Vedclass Test Series

Exam Paper Generator

Online Exam Module