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Application of Newtons laws

Question

In the figure shown, the acceleration of A is 2 m/s2 to left and acceleration of B is 1 m/s2 to left.

The magnitude of acceleration of C in m/s2 is _________

Moderate
Solution

Let displacement of A is x1, B is x2 and that of C is x3 in a given time. Now length of string should remain same. 

So initial length = final length

I1+I2+I3+I4+I5=I1+x1x2+I2x2+I3+x1+I4+x3+I5+x3

 x3=x2x1 Differentiating twice: a3=a2a1a3=12=1m/s2

 So acceleration of C is 1m/s2 upwards. 

 



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