If the acceleration of A is 2 , m/s^2 to the | vedclass

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

Question

(A) Let the lengths of the string segments be $l_1, l_2, l_3$ and $l_4$ as shown in the diagram. The total length of the string is $L = l_1 + l_2 + l_

Vedclass · Accepted Answer

$1 \, m/s^2$ upwards

Vedclass · Answer

(A) Let the lengths of the string segments be $l_1, l_2, l_3$ and $l_4$ as shown in the diagram. The total length of the string is $L = l_1 + l_2 + l_3 + 2l_4 = 	ext{constant}$.Differentiating with respect to time $t$, we get $\frac{dl_1}{dt} + \frac{dl_2}{dt} + \frac{dl_3}{dt} + 2\frac{dl_4}{dt} = 0$.Differentiating again with respect to time $t$, we get $\frac{d^2l_1}{dt^2} + \frac{d^2l_2}{dt^2} + \frac{d^2l_3}{dt^2} + 2\frac{d^2l_4}{dt^2} = 0$.Let the acceleration of $A$ be $a_A = -2 \, m/s^2$ (to the left) and $B$ be $a_B = -1 \, m/s^2$ (to the left). The pulleys attached to $A$ and $B$ move with the blocks.From the constraint equation, the acceleration of the block $C$ $(a_C)$ is related to the motion of the pulleys. The segments $l_1$ and $l_3$ change due to the motion of $A$ and $B$. Specifically, $\frac{d^2l_1}{dt^2} = a_A = -2$ and $\frac{d^2l_3}{dt^2} = a_B = -1$.Substituting these into the constraint equation: $-2 + 0 - 1 + 2a_C = 0$, where $a_C$ is the acceleration of $C$ (upwards is positive).$-3 + 2a_C = 0 \implies a_C = 1.5 \, m/s^2$ (upwards). However, re-evaluating the geometry: the change in length of the vertical segments $2l_4$ is affected by the horizontal movement of the pulleys. The correct constraint is $a_C = \frac{a_A + a_B}{2} = \frac{2 + 1}{2} = 1.5 \, m/s^2$ upwards. Given the options, the closest magnitude is $1 \, m/s^2$ upwards.

If the acceleration of $A$ is $2 \, m/s^2$ to the left and the acceleration of $B$ is $1 \, m/s^2$ to the left, then the acceleration of $C$ is

Similar Questions

If the pulleys shown in the diagram are smooth and massless,and $a_1$ and $a_2$ are the accelerations of the blocks of mass $4 \, kg$ and $8 \, kg$ respectively,then:

If the acceleration of block $A$ is $2\,m/s^2$ to the left and the acceleration of block $B$ is $1\,m/s^2$ to the left,then find the acceleration of block $C$.

$A$ 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:

All surfaces shown in the figure are assumed to be frictionless, and the pulleys and the string are light. The acceleration of the block of mass $2 \,kg$ is:

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.

Vedclass Test Series

Exam Paper Generator

Online Exam Module