Two bodies of equal masses are attached to the end of the string which passes over a pulley such that bodies hang vertically. If a mass of 0.2 Kg is added in one of them and acceleration of of system is 0.2m/s then what are the of values of masses.
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Answer:
Force balance equations for two weights can be written as:
T
1
=m
1
g−m
1
a---------(i)
and T
2
=m
2
a+m
2
g----------(ii)
(ii)-(i), we get:
T
1
−T
2
=(m
1
−m
2
)g−(m
1
+m
2
)a------------(iii)
As torque, τ=Iα, we have:
(T
1
−T
2
)R=(
2
1
MR
2
).
R
a
or, T
1
−T
2
=
2
Ma
Substituting this in equation (iii), we get:
2
Ma
=(m
1
−m
2
)g−(m
1
+m
2
)a
or, a=
m
1
+m
2
+(m/2)
(m
1
−m
2
)g
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