Question

Two masses $M$ and $m(M>m)$ are joined by a light string passing over a smooth light pulley. If the blocks are allowed to move for some time, after which $M$ is stopped momentarily (brought to rest and released at once). After this:

• A. both blocks will move with the same acceleration
• B. the strings will become taut (under tension) again when the blocks acquire the same speed
• C. the string will become taut again when the blocks cover equal distances
• D. at the instant when the string becomes taut again, there may be some exchange of impulse between the string and blocks

Answer 1

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

The correct options are
A both blocks will move with the same acceleration
B the strings will become taut (under tension) again when the blocks acquire the same speed
C the string will become taut again when the blocks cover equal distances

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 $\left(1\right)$, $T=m\frac{M-m}{M+m}g+mg=\frac{2Mmg}{M+m}$
when taut again they cover same distance because,$S=\frac{1}{2}a{t}^2$ for both masses.
Ans:(A), (B), (C)