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FIND ACCELERATION OF BLOCK OF MASS 4M JUST AFTER THE SYSTEM IS RELEASED FROM REST

FIND ACCELERATION OF BLOCK OF MASS 4M JUST AFTER THE SYSTEM IS RELEASED FROM REST

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Grade:12th pass

2 Answers

Arun
25750 Points
5 years ago
Dear Utkarsh
 
Figure attached is unclear in my system. Please check and re attach the image
 
I will be hapy to help you.
 
Regards
Arun
Piyush Kumar Maurya
65 Points
5 years ago
First of all calculate theta , it will come out to be 37°.
Let T be the tension in string connected to mass m block. Since the string connected to 4m block is at an angle , we will resolve it, it comes out to be Tcos theta acting vertically upwards. let 'a' be the acceleration of 4m block downwards. 
So by constrained 
Tm * am  = T4m * a4m  ( tension *acceleration must bemust be equal for both mass m and 4m block)
T *am = Tcos theta *a 
am = a*cos theta 
free body diagram of 4 m block-
4mg - 2Tcos theta = 4ma.          
Here theta = 37° , so cos theta = 4/5 
4mg - 8T/5 = 4ma .        (i)
 
Free body diagram of m block
T - mg = ma cos theta
T - mg = ma 4/5 .         (ii).
On solving these two equations 
a = 5g/11 (Ans)
 
 
 

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