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Question

For the system shown in the figure, the pulley is smooth and massless, the string is massless and inextensible. If the acceleration of the system is (a) then, find out the ratio of tensions T1 and T2.
(Take g=10 m/s2)

A
20:3
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B
5:1
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C
3:1
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D
5:2
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Solution

The correct option is C 3:1

Here, net pulling force will be
(weight of 4 kg and 2 kg blocks on one side) (weight of 4 kg block on the other side ).
Acceleration of the system is given by a;
a=Net pulling forceTotal mass

a=(2×10)+(4×10)(4×10)2+4+4

a=2010=2 m/s2

For T1:
From FBD of 4 kg block,
T140=4a
T1=40+4a
T1=40+(4×2)=48 N

For T2:
From FBD of 2 kg block,

mgT2=2a
T2=202a
T2=202×2=16 N

T1T2=(4816)=3:1

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