First slide

Constraints

Question

Two masses each equal to m are lying on X-axis at (- a,0) and (+ a, 0) respectively as shown in fig.
They are connected by a light string. A force F is applied at the origin and along the Y-axis. As a result, the masses move towards each other What is the acceleration of each mass ? Assume the instantaneous position of the masses as (- x,0) and {x, 0) respectively

Moderate

A

$\frac{F}{m} \cdot \frac{x}{\sqrt{(a^{2} - x^{2})}}$
B

$\frac{F}{2 m} \cdot \frac{x}{\sqrt{(a^{2} - x^{2})}}$
C

$\frac{2 F}{m} \cdot \frac{x}{\sqrt{(a^{2} - x^{2})}}$
D

$\frac{2 F}{m} \cdot \frac{\sqrt{(a^{2} - x^{2})}}{x}$

Solution

See figure.
From figure $F = 2 Tcos θ or T = F / (2 \cos θ)$
The force responsible for motion of masses on X-axis is $Tsin θ$
$\begin{aligned} ∴ ma & = Tsin θ = \frac{F}{2 \cos θ} \times \sin θ \\ = \frac{F}{2} \tan θ = \frac{F}{2} \times \frac{OB}{OA} = \frac{F}{2} \times \frac{x}{\sqrt{(a^{2} - x^{2})}} \end{aligned}$
$So, a = \frac{F}{2 m} \times \frac{x}{\sqrt{(a^{2} - x^{2})}} .$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App