Question

Two unequal masses of $1kg$ and $2kg$ are connected by a string going over clamped light smooth pulley as shown in figure. The system is released from rest. The larger mass is stropped for a moment $1.0s$ after the system is set in motion. Find the time elapsed before the string is tight again.

• A. $\frac{1}{3}s$
• B. $1s$
• C. $2s$
• D. $3s$

Answer 1

The correct option is A $\frac{1}{3}s$

Tension in the string $T=mg=$$1\times g=gN$

Forces acting on $2kg$ block:

Upward force $=T=gN$

Downward force $=m_{2}g$$=2\times g=2gN$

Net force $=2g-g=gN$ downward

So, net force on the system is $gN$.

Lets assume that acceleration of the blocks is $a$ after larger block is stropped.

Net force $=$ total mass $\times$ acceleration

$g=(1+2)\times a$

$⟹a=\frac{g}{3}$

At $t=1sec$

Velocity of $1kg$ block

$v_1=u+at$

$v_1=0+\frac{g}{3}\times 1$

$⟹v_1=\frac{g}{3}$

As velocity of $1kg$ block becomes zero, the string is tight again.

Final velocity of $1kg$ block $=0m/s$

$0=$$\frac{g}{3}$$-gt$; acceleration is only due to gravitational force so its value will be $-g$

$⟹t=\frac{1}{3}$ sec

Hence, the string is tight again at $\frac{1}{3}$ sec.