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  4. Two masses M1=5 kg and M2=10 kg are connected at the ends of an inextensible string passing over a frictionless pulley as shown. When the masses are released, then the acceleration of the masses will be

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Q. Two masses $M_{1}=5\, kg$ and $M_{2}=10\, kg$ are connected at the ends of an inextensible string passing over a frictionless pulley as shown. When the masses are released, then the acceleration of the masses will bePhysics Question Image

AIIMSAIIMS 2010Laws of Motion

Solution:

Since $M _{2}> M _{1}$, therefore $M _{2}$ moves downwards and $M _{1}$ moves upwards with an acceleration a as shown in the figure.
image
Free body diagram of $M_1$
image
The equation of motion for $M_1$ is
$T - M_1g = M_1a \,\dots$(i)
Free body diagram of $M_2$
image
The equation of motion for $M _{2}$ is
$M_{2} g-T=M_{2} a \,\ldots \ldots(ii)$
Adding (i) and (ii), we get
$a=\frac{\left(M_{2}-M_{1}\right) g}{M_{2}+M_{1}}$
$=\frac{(10-5) g}{(10+5)}=\frac{g}{3}$