Two bodies of masses 10.2 kg and 4.5 kg are attached to the two ends of a string which passes over a pulley in such a way that the body of mass 10.2 kg lies on a smooth horizontal surface and the other body hangs vertically. Find the acceleration of the bodies, the tension of the string and also the force which the surface exerts on the body of mass 10.2
kg
(Ans. 3 m/s, 30.6 N. 99.96 N).
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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
Explanation:
assume 10.2 as m1
and 4.5 as m2
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