In the figure, block A and B of masses 2m and m are connected with a string and system is hanged vertically with the help of a spring. Spring has negligible mass. Find out magnitude of acceleration of masses 2m and m just after the instant when the string of mass m is cut [AIIMS 2018]

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In the figure, block A and B of masses 2m and m are connected with a string and system is hanged vertically with the help of a spring. Spring has negligible mass. Find out magnitude of acceleration of masses 2m and m just after the instant when the string of mass m is cut [AIIMS 2018]

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a

g, $\frac{g}{2}$

b

$\frac{g}{2}$ , $\frac{g}{2}$

c

g,g

d

$\frac{g}{2}$ , g

answer is C.

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Detailed Solution

When the system is in equilibrium, then the spring force is 3 mg. When the string is cut, then net force on block A

$= 3 m g - 2 m g = m g$

Hence, acceleration of block A at that instant,

$a = \frac{Force on block A}{Mass of block A} = \frac{m g}{2 m} = \frac{g}{2}$

When string is cut, then block B falls freely with an acceleration equal to g.

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In the figure, block A and B of masses 2m and m are connected with a string and system is hanged vertically with the help of a spring. Spring has negligible mass. Find out magnitude of acceleration of masses 2m and m just after the instant when the string of mass m is cut [AIIMS 2018]