# Three masses are connected as shown, with weightless and inextensible ropes over a frictionless pulley. The planes where ( m\_1 ) and ( m\_2 ) lie are horizontal and frictionless. When the system is released, ( m\_3 ) moves downward. Find the acceleration of

**URL:** <https://sorumatik.co/t/three-masses-are-connected-as-shown-with-weightless-and-inextensible-ropes-over-a-frictionless-pulley-the-planes-where-m-1-and-m-2-lie-are-horizontal-and-frictionless-when-the-system-is-released-m-3-moves-downward-find-the-acceleration-of/83853>\
**Category:** Üniversite\
**Created:** [Temmuz 24, 2024, 6:07ös UTC](https://sorumatik.co/t/three-masses-are-connected-as-shown-with-weightless-and-inextensible-ropes-over-a-frictionless-pulley-the-planes-where-m-1-and-m-2-lie-are-horizontal-and-frictionless-when-the-system-is-released-m-3-moves-downward-find-the-acceleration-of/83853 "2024-07-24T18:07:16Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![Ali\_Kaya\_Akin](https://sorumatik.co/letter_avatar_proxy/v4/letter/a/ecb155/32.png) [@Ali\_Kaya\_Akin](https://sorumatik.co/u/Ali_Kaya_Akin)\
**Post date:** [Temmuz 24, 2024, 6:07ös UTC](https://sorumatik.co/t/three-masses-are-connected-as-shown-with-weightless-and-inextensible-ropes-over-a-frictionless-pulley-the-planes-where-m-1-and-m-2-lie-are-horizontal-and-frictionless-when-the-system-is-released-m-3-moves-downward-find-the-acceleration-of/83853/1 "2024-07-24T18:07:16Z")

</div>

@sorumatikbot

 ![Ekran görüntüsü 2024-07-24 210703](https://sorumatik.co/uploads/default/original/3X/8/3/831ba2b710f9af42e3ed28249aa457f6702afd54.jpeg)

---

<div class="post-metadata">

**Author:** ![Sorumatik\_Ogretmen](https://sorumatik.co/user_avatar/sorumatik.co/sorumatik_ogretmen/32/30517_2.png) [@Sorumatik\_Ogretmen](https://sorumatik.co/u/Sorumatik_Ogretmen)\
**Post date:** [Temmuz 24, 2024, 6:07ös UTC](https://sorumatik.co/t/three-masses-are-connected-as-shown-with-weightless-and-inextensible-ropes-over-a-frictionless-pulley-the-planes-where-m-1-and-m-2-lie-are-horizontal-and-frictionless-when-the-system-is-released-m-3-moves-downward-find-the-acceleration-of/83853/2 "2024-07-24T18:07:34Z")

</div>

## **Ali\_Kaya\_Akin’s Question**

Ali\_Kaya\_Akin shared the following problem:

_Three masses are connected as shown, with weightless and inextensible ropes over a frictionless pulley. The planes where m\_1 and m\_2 lie are horizontal and frictionless. When the system is released, m\_3 moves downward. Find the acceleration of the system in terms of the gravitational acceleration g ._

The choices are:  
A) \frac{2}{5}g   
B) \frac{1}{5}g   
C) \frac{1}{2}g   
D) \frac{1}{4}g   
E) \frac{1}{3}g

**Answer:**

To determine the acceleration of the system, we must apply Newton’s second law to each of the masses.

1. **Equation of motion for m\_3 :**

2. **Equation of motion for m\_1 and m\_2 :**

3. **Combining the forces:**

4. **Solving for a :**

Therefore, the correct answer is \boxed{\frac{1}{2}g} .