What horizontal force must be applied to the cart shown in the figure* given below so that the blocks remain stationary relativ to the cart? Assume all surfaces of the wheels and the pulley are frictionless.

* - to get the image,, go to google images and type - what horizontal force must be applied to the cart and the first image is the image of this question. Since i could not copy and paste the link in the editor and inserting image would take some time to be veiwable on the forum, this was m last resort. So please help me out guys.

let acceleration of the system be a

a=F/(m1 + m2)

let tension in string be T

then from f.b.d of m1

T=m1*a so that it remains at rest relative to cart  (note that our reference frame is the cart, hence a pseudo force will act on each of the masses towards the left)  ............ (1)

where m1*a is the pseudo force acting on m1

again from f.b.d of m2

T=m2*g where g is the acc due to gravity .....................(2)

from (1) and (2)

m1*a=m2*g

substituting the value of a  you will get

F=((m1 + m2)m2*g)/m1 which is ur required answer

im very sorry, i had not noticed that the cart had mass...

not much change is required though, jst calculat a as a=F/(M + m1 + m2)

then proceed...