The system shown in the figure is in equilibrium and all the blocks are at rest. Assume that the masses of the strings, the pulley and the spring are negligible with respect to the masses of the blocks and friction is absent. Find the acceleration of block C , just after cutting the string 1 . [ g=10ms- 2 ]

Question

The system shown in the figure is in equilibrium and all the blocks are at rest. Assume that the masses of the strings, the pulley and the spring are negligible with respect to the masses of the blocks and friction is absent. Find the acceleration of block C , just after cutting the string 1 . [ g=10ms- 2 ] <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-7aibkhooaodv.png" /> (A) 5 ms- 2 (B) 3 ms- 2 (C) 2 ms- 2 (D) 6 ms- 2

Tardigrade Admin · Accepted Answer

Just after cutting the string 1 the extension of the string will remain same as it was before cutting the string '1'. So, we can take string force on block is equal '2g'.
Now making F.B.D of block 'B'.

3 g - T = 1 a

.... (i)

Making F.B.D of block 'c'
Solution

T = 5 a

.... (ii)
From (i) and (ii)

a = \frac{g}{2} = 5 m s^{- 2}

Making F.B.D of block 'c' Solution

T=5a .... (ii) From (i) and (ii) a=(g/2)=5 m s- 2

$5 m s^{- 2}$

$3 m s^{- 2}$

$2 m s^{- 2}$

$6 m s^{- 2}$

5ms−2

3ms−2

2ms−2

6ms−2

Just after cutting the string 1 the extension of the string will remain same as it was before cutting the string '1'. So, we can take string force on block is equal '2g'. Now making F.B.D of block 'B'. 3g−T=1a .... (i) Making F.B.D of block 'c' T=5a .... (ii) From (i) and (ii) a=2g​=5ms−2

$5 m s^{- 2}$

$3 m s^{- 2}$

$2 m s^{- 2}$

$6 m s^{- 2}$