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# Two blocks of 100 kg and 50 kg connected by a massless string passing over a frictionless pulley rests on frictionless inclined plates inclined at angles $30^{\circ}$ and $60^{\circ}$ what is the acceleration and which way the system moves? $(g=10 m/s)$

$\begin{array}{1 1} 1m/s,left \\ 0.664\;m/s \;right \\ 0.866\;m/s,\;left \\ 0.446\;m/s,\;left \end{array}$

For 100 kg mass:
$100g\; \sin\; 30^{\circ}-T=100 a$
$500-T-100 a$-----(1)
For 50 kg mass
$T-50 g\;\sin 60=a \times 50$
$T-433=50a$-----(2)
$150 a=67$
$a=0.446 ms^{-2}$
a is towards left as shown
Hence d is the correct answer.
edited May 27, 2014