find the tension in the light string in the following cases two blocks a and b are connected by a light string passing through a smooth pulley.
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From FBD of A and B, shown in Fig. the block A is just to slip, the friction will reach to its limiting value
f
lim
=μN (i)
From FBD of A,
N+Tsinθ=m
A
g (ii)
Tcosθ=f
max
=μN (iii)
From (ii), N=m
A
g−Tsinθ (iv)
From (iii) and (iv),
Tcosθ=μm
A
g−Tsinθ (v)
T(cosθ+μsinθ)=μm
A
g (vi)
From FBD of B, T= m
B
g (vii)
Taking ratio of (vi) and (vii),
Cosθ+μsinθ
μ
=
m
A
m
B
∴
m
B
m
A
=
μ
Cosθ+μSinθ
=
(0.5)
Cos37
0
+(0.5)Sin37
0
=
5
11
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