A block of mass m2 = 12kg on a rough horizontal surface ( µK = 0.42 ) is connected to a ball of mass m1 = 6 Kg by a lightweight cord over a lightweight pulley as shown in the figure, A force F= 350 N at an angle θ = 30ᵒ is applied to the block and the block slides to the right, Determine the magnitude of the acceleration of the system and the tension in the cord.
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Class 11
>>Physics
>>Laws of Motion
>>Application of Newton's Laws of Motion
>>A block of mass m2 on a rough, horizon
Question
A block of mass m
2
on a rough, horizontal surface is connected toa aball of mass m
1
by a lightweight cord over a lightweight, frictionless pulley as shown in Figure. A force of magnitude F at an angle θ with the horizontal is applied to the block as shown, and the block slides to the right. The coefficient of kinetic friction between the block and surface is μk
˙
Determine the magnitude of the acceleration of the two objects.
1164683
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A
a=
m
1
+m
2
3F(cosθ+μ
1
sinθ)−(m
1
+μ
2
m
2
)g
B
a=
m
1
+m
2
F(cosθ+μ
1
sinθ)−(m
1
+μ
2
m
2
)g
C
a=
m
1
+m
2
2F(cosθ+μ
1
sinθ)−(m
1
+μ
2
m
2
)g
D
a=
m
1
+m
2
4F(cosθ+μ
1
sinθ)−(m
1
+μ
2
m
2
)g
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Solution
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Correct option is B)
REF.Image
Solution
Consider the following ABD
From,
T−m
1
g=m
1
a ____ (i)
For m
2
′
Fcosθ−T−μN=m
2
a ____ (ii)
N=μ
2
g−Fsinθ ___ (iii)
Adding (i), (ii) and (iii), we get
Fcosθ+Fsinθμ−μ
2
gμ−m
1
g=m
1
a+m
2
a
⇒
m
1
+m
2
F(cosθ+sinθμ)−g(m
1
+m
2
a)
=a
Option - B is correct