Question

(i)in a simple attwood machine 2 unequal masses m1 and m2 are connected by a string going over a clamped light smooth pulley.in typical arrangement m1=300g and m2=600g
*thye distance travelled by the first block in first 2 seconds is (the attachemtn is valid for first uestion only)
*the tension in the string is
*draw fbds os m1 ,m2 and pulley
(ii)look at second attachement of integer questions
(iii)2 masses m and M respectively are connected by a light string passing over a smooth pulley when set free m moves up by 1.4 m in 2 secthe ratio of m/M is 

Answer 1

equations of motion or dynamics for the diagram/question are:

T - m1 g = m1 a
m2 g - T = m2 a

=>  a = (m2 - m1) g / (m1 + m2)
           =  (600 - 300) * 10 / (600 + 300) = 10/3 m/sec/sec

   If  u = 0 ,  and  t = 2 sec.
       s = u t + 1/2  a t^2 = 20/3 meters
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solving the first two equations
       T = 2 m1 * m2 * g / (m1 + m2)
           = 2 * 600 * 300 * 10 / 900 = 4 000 newtons
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iii)
       s = 1.4 meters
       t = 2 sec.
         u = 0.
     s = ut + 1/2 a t^2  =>
      a = 2 * 1.4 / 4 = 0.7 meters/sec/sec
      
     a  =  (m2 - m1) g / ( m1 + m2)
         =  (m2/m1 - 1) g / (m2 / m1  + 1 )

  =>    m2/m1 + 1 =  (m2/m1 -1 )  * g/a
          m2/m1  [g/a - 1]  =  1 + g/a
         m2 / m1  =  (a + g) / (g - a)

          m2 / m1  =  (10 + 0.7) / (10 - 0.7)  = 10.7 / 9.3 

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Block B is on top of block  A.

   Block A has mass    m.      So its acceleration =  10 Newtons / m
   It moves by 20 cm  before block B falls.
         u = 0
 
       s = u t + 1/2 a t^2
 
       20 cm = 0 + 1/2 * (10/m) * t^2
       find t from this by substituting the value of m.
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In the question Is the rod AB is resting  on a surface  OB ??

it is not clear what  OB is..  is there friction at the points  A and B ??

is it possible that n = 1  or  n = 1/2 ??