Two block of equal mass m are connected byan unstretched spring and the sytem is keptat rest on a frictionless horizontal surface. A constant force F is applied on one of the blocks puling it away from the other as shown in figure. a.Find the positon of the centre of mass at time t. b.If the extansion of the spring is x_0 at time t find the displacement of the two blocks at this instant.

Two block of equal mass m are connected byan unstretched spring and th

1.	Two block of equal mass m are connected byan unstretched spring and the sytem is keptat rest on a frictionless horizontal surface. A constant force F is applied on one of the blocks puling it away from the other as shown in figure. a.Find the positon of the centre of mass at time t. b.If the extansion of the spring is x_0 at time t find the displacement of the two blocks at this instant.
Answer» Solution :a. The acceleration of the centre of MASS is given by `a_(CM) =F/M=F/(2M) ` The position of the centre of mass at time to is `x=1/2a_(CM) t^2=(Ft^2)/(4m)` b. Suppose the displacement of the first block is `x_1` ANDTHAT of the SECOND is `x_2`. As the centre of mass is at x, we should have `x=(mx_1+mx_2)/(2m)` `or, (Ft^2)/(4m)=(x_1+x_2)/2` `or, x_1+x_2=(Ft^2)/(2m)` .......i the extension of th spring is `x_2-x_1`. therefore `x_2-x_1=x_0` ......ii ltbr `from i and ii `x_1=1/2((Ft^2)/(2m)-x_0)` and `x_2=1/2((Ft^2)/(2m)+x_0)`.