Question

All surfaces are assumed to be frictionless. Calculate
the horizontal force F that must be applied so that
m1 and m2 do not move relative to m3 is :-
​

Answer 1

1. (m1+m2+m3)m2gm12. (m1+m2)m2gm13. (m2+m3)m1gm24. (m1+m3)m1gm2

let that force be F accn of the system be a=Fm1+m2+m3let the tension at this situation is TT=m2gT=m1am2g=m1aa=m2gm1m2gm1=Fm1+m2+m3F=m2gm1(m1+m2+m3)Regards

Answer 2

Answer:

$F =\dfrac{(m_1+ m_2 +m_3)m_2g}{m_1}$

Explanation:

For no relative motion between blocks.The horizontal acceleration of block m₁  and m₃ should be same also the vertical acceleration of block m₂ should be zero.

Lets T is the tension in string

For block  m₁  

T = m₁  a                 ( a is the acceleration)

Fro block m₂

T -  m₂ g = 0

m₁  a  -  m₂ g = 0

 a =  m₂ g / m₁

For no motion between block

F = (m₁ + m₂ +m₃) a

F = (m₁ + m₂ +m₃) m₂ g / m₁

$F =\dfrac{(m_1+ m_2 +m_3)m_2g}{m_1}$