from the question i thought that the two blocks would be carrying out uniform circular motion about a on the string such that the centripetal force (tension) acting on each block would be equal:
$$ \frac{m_{1} v_{1}^{2}}{1 - x} = \frac{m_{2} v_{2}^{2}}{x} $$
and on solving for x (taking m1 as 3...
sorry ill try to make it clearer, (Fg=GmM/x2) (assuming velocity of M to be V and velocity of m to be v at a point)
for the mass M
Ma= Fg
M(dV/dt)= Fg
M(dV/dx)*(dx/dt)=Fg
M(dV/dx)*V=Fg
MVdV=Fg*dx
MV2/2=Fg*dx .....(1)
for the mass m
m(-a)= -Fg
m(dv/dt)= Fg
m(dv/dx)*(dx/dt)=Fg
m(dv/dx)*v=Fg...
yes, our professor said to use conservation of momentum/ conservation of velocity of com, and i understood the method and the reasoning behind it, the part im facing a problem with is, why upon using the method i used am i getting a different answer.
our professor told us to solve this using the fact that the velocity of centre of mass (com) will be 0, however before he said this i had taken a different approach and did this:
ma=GmM/r^2
m(dv/dr)*(dr/dt)= Fg (taking GmM/r^2 as Fg for now)
1/2(mv^2)= Fg dr
and since for M force= -Fg...