Question

In the system shown, initially the block A of mass m is hanging at rest
and the block B of mass 2m is on the ground. The pulleys have negligible
masses and negligible friction, and the thread is extremely light and
almost inextensible. Acceleration due to gravity is g. The free end of the
thread is pulled upwards with a constant force. When it acquires a
speed u, find speeds of both the blocks.



aukat hai toh solve kar​

Answer 1

since free body diagram of both masses are given

for mass A with respect to mass B

F¹=2mg-T (mass B).............(1)

F²=T-mg (mass A).......... (2)

for mass B with respect to mass A

F¹=T-2mg (mass B).........(3)

F²=mg-T (mass A)............ (4)

add equation (1),(2)

F¹+F²=2mg-T+T-mg

ma+2ma=2mg-T+T-mg (T cancel out each other)

3ma=2mg-mg

3ma=mg

a=mg/3m

a=g/3

from equation of motion

v=u+at

since t is time for which act

v=u+gt/3

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