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  4. Two particles A and B each of mass m are attached by a light inextensible string of length 2l . The whole system lies on a smooth horizontal table with B initially at a distance l from A . The particle at the end B is projected across the table with speed u perpendicular to AB . The velocity of the ball A just after the string is taut, is <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-oohtygpt5j6b.png />

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Q. Two particles $A$ and $B$ each of mass $m$ are attached by a light inextensible string of length $2l$ . The whole system lies on a smooth horizontal table with $B$ initially at a distance $l$ from $A$ . The particle at the end $B$ is projected across the table with speed $u$ perpendicular to $AB$ . The velocity of the ball $A$ just after the string is taut, is

Question

NTA AbhyasNTA Abhyas 2020

Solution:

Solution
When the string jerk tight both particles begin to move with velocity components $v$ in the direction $AB$ . Using conservation of momentum in the direction $AB$
$mucos \, 30 ^\circ =mv+mv$
or $v=\frac{u \sqrt{3}}{4}$
Hence, the velocity of ball $A$ just after the jerk is $\frac{u \sqrt{3}}{4}$