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Question

Two masses 5 Kg and 2 Kg connected by a string are at rest on a smooth horizontal surface. A constant force 1 N is applied on 5 Kg mass as shown in the figure. Two second later the string connecting the masses is cut but F continues to act. After two more seconds, find the velocity of both 2 Kg body and acceleration of 5 Kg block.
1075378_30dbc122d50c4b0287c6925a5f4634fd.png

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Solution

The block will be lifted only when the tension of string exceeds the gravitational pull on them.

gravitational force =mg+Mg
=2kg×10m/s²+5kg×10m/s²=70N

Let's check , F2T=0 [ see free body diagram as shown in figure ]
given, F=110N
1102T=0=>T=55N

tension is greater than gravitational pull { e.g., 55N>50N and 55N>20N

so, use Newton's law of motion separately for both blocks

acceleration of block of mass 2kg is a ,
Tmg=ma
552×10=2×a
5520=2a=>a=17.5m/s²

acceleration of block of mass 5kg is a',
TMg=Ma
555×10=5a
5550=5a=>a=1m/s²


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