Question

Two masses $M$ and $m$ ($M>m$) are joined by a light string passing over a smooth light pulley. Then:

• A. the acceleration of each block is $\left(\frac{M-m}{M+m}\right)g$
• B. the tension in the string is $\frac{2Mmg}{M+m}$
• C. the centre of mass of the '$Mplusm$' system moves down with an acceleration of g ${\left(\frac{M-m}{M+m}\right)}^2$
• D. the tension in the string by which the pulley is attached to the roof is $(M+m)g$

Answer 1

Answer: (A), (B), (C)

The correct options are
A the acceleration of each block is $\left(\frac{M-m}{M+m}\right)g$
B the tension in the string is $\frac{2Mmg}{M+m}$
C the centre of mass of the '$Mplusm$' system moves down with an acceleration of g ${\left(\frac{M-m}{M+m}\right)}^2$

For mass $m:ma=T-mg....\left(1\right)$

For mass $M:Ma=Mg-T.....\left(2\right)$

$\left(1\right)+\left(2\right)$, $a(M+m)=(M-m)g\Rightarrow a=\frac{M-m}{M+m}g$

Thus, magnitude of acceleration each block , $a=\frac{M-m}{M+m}g$

put value of $a$ in $\left(1\right)$, $T=m\frac{M-m}{M+m}g+mg=\frac{2Mmg}{M+m}$

$a_{cm}=\frac{Ma-ma}{M+m}=(\frac{M-m}{M+m}{)}^{2}g$

Ans:(A), (B), (C)