Two unequal masses are connected on two sides of a light string passing over a light and smooth pulley as shown in figure. The system is released from rest. The larger mass is stopped $$1.0$$ second after the system is set into motion and then released immediately. The time elapsed before the string is tight again is: Take g $$=$$ $$10$$ $$m/s2$$

Question

Two unequal masses are connected on two sides of a light string passing over a light and smooth pulley as shown in figure. The system is released from rest. The larger mass is stopped $$1.0$$ second after the system is set into motion  and then released immediately. The time elapsed before the string is tight again is: Take g $$=$$ $$10$$ $$m/s2$$

Infinity Learn · Accepted Answer

Acceleration of the system:a $$=$$ $$m2-m1m2+m1g$$ $$=$$ $$103m/s2Velocity$$ of both the blocks at t $$=$$ $$1$$ s will bevo $$=$$ at $$=$$ $$103$$×$$1$$ $$=$$ $$103m/sNow$$ at this moment, velocity of $$2$$ kg block becomes zero, while that of I kg block is $$103m/s$$. upwards.Hence, string becomes tight again whenDisplacement of I kg block $$=$$ displacement of $$2$$ kg blockor $$v0t-12gt2$$ $$=$$ $$12gt2$$

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