# Answer Part B) only The figure represents a vertical cross section of a smooth block of mass M with PQ and RS inclined at an angle Alpha to the horizontal, and QR and PS being horizontal. A...

**Answer Part B) only**

The figure represents a vertical cross section of a smooth block of mass M with PQ and RS inclined at an angle Alpha to the horizontal, and QR and PS being horizontal. A smooth light inelastic string passes over two small smooth pulleys at Q and R . Two small smooth particles A and C of masses m_1 and m_3 respectively are attached to the ends of the string. A third small smooth particle B of mass m_2 is attached to the string in between Q and R .The block is free to move on a smooth horizontal plane.

**A)**

Write downequations to determine the acceleration of the block relative to the plane, the accelerations of the particles relative to the block, and the tensions in the portions AB and BC of the string.

**B)**

If mass of the particle B is negligible, show that the tensions in the two portions AB and BC of the string are the same .

**C)**

If, further the mass of the block is also negligible, show that each of the magnitudes of the reactions of the block on A and C is equal to `(2m_1m_3)/ (m_1+m_3)g cos alpha` .

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### 1 Answer

Consider motion of particle B along x-direction (see the attached image),

`F_(net)=T_1-T_3=m_2*a`

Evidently, when `m_2` is negligible,

`m_2*a~~0`

Hence,

`T_1-T_3=0`

`rArr T_1=T_3`

Tensions in the two portions AB and BC of the string are the same.