Question

Two blocks $A$ and $B$ having equal masses, M each, are joined by means of a slacked string passing over a massless pulley fixed to a ceiling. The system is released from rest and it becomes taut when $B$ falls a distance $0.5m$. If the magnitude of impulse on the pulley by the clamp during the small interval while string becomes taut is $\frac{4}{3}\sqrt{b}Ns$, find the value of $b$.

• A. $\frac{25M^2}{2}$
• B. $\frac{45M^2}{2}$
• C. $\frac{35M^2}{2}$
• D. None of these
  

Answer 1

The correct option is B $\frac{45M^2}{2}$

Velocity of block A and B when they traveled .5 m is $V^2=2gh=2g\times 0.5=g$

$V=\sqrt{g}$

Now change in momentum of block B is $P=mV=M\sqrt{g}$

Now change in momentum of block A is $P=mV=M\sqrt{g}$

Total change in momentum is equal to impulse

$I=\frac{4\sqrt{b}}{3}=2M\sqrt{10}$

$\therefore b=\frac{45M^2}{2}$