Two blocks of massesare arranged with an ideal pulley and a massless string as shown, with the block of masson a rough horizontal table. The required coefficient of friction between the block and the table such that the blocks can move with constant velocity is
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Solution
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Correct option is
B
3.3
Given that,
Mass of block A=10 kg
Kinetic friction μ=0.2
Now, according to diagram
Now, the component of the weight in the direction of the incline
W=m
A
gsinθ
T=F
f
−W....(I)
When the force of friction
F
f
=μ
k
N
F
f
=μ
k
(m
A
gcosθ)
Now, put the value in equation (I)
The tension is
T=m
A
gsin30
0
−μ
k
m
A
gcos30
0
We know that,
T−m
B
g=0
T=m
B
g
So,
m
B
g=m
A
g(sin30
0
−0.2×cos30
0
)
m
B
=10×(
2
1
−0.2×
2
3
)
m
B
=10×(0.5−0.1732)
m
B
=10×0.3268
m
B
=3.268
m
B
=3.3kg
Hence, the mass of block B is 3.3 kg
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