Question

Two masses $5Kg$ and $2Kg$ connected by a string are at rest on a smooth horizontal surface. A constant force $1N$ is applied on $5Kg$ 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 $2Kg$ body and acceleration of $5Kg$ block.

Answer 1

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

gravitational force =$mg+Mg$

$=2kg\times 10m/s²+5kg\times 10m/s²=70N$

Let's check , $F-2T=0$ [ see free body diagram as shown in figure ]

given, $F=110N$

$110-2T=0=>T=55N$

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 ,

$T-mg=ma$

$55-2\times 10=2\times a$

$55-20=2a=>a=17.5m/s²$

acceleration of block of mass 5kg is a',

$T-Mg=M{a}^{\prime }$

$55-5\times 10=5a$

$55-50=5a=>a=1m/s²$