The string beween blocks of mass m and 2m is massless and inextensible. The system is suspended by a massless spring as shown. If the string is cut find the magnitudes of accelerations of mass 2m and m (immediately after cutting):

Options

A. g.g
B. `g,(g)/(2)`
C. `(g)/(2),g`
D. `(g)/(2),(g)/(2)`

Answer

c

Explanation

By equilibrium of mass m, T. = mg

By equilibrium of 2m, T=2 mg - T
From (i) & (ii), `T = 2mg - mg = mg`
When the string is cut:
For mass m:
`F_(net) = ma_(m)`
`implies mg = ma_(m)`
`impliesa_(m)=g`
For mass 2m :
`F_(net) = 2ma_(2m)`
` implies 2mg - T = 2ma_(2m )`
`= 2mg - mg = 2ma_(2m)`
`impliesa_(2m)=(g)/(2)`
Hence choice is (C).