If the system is initially at rest. Find the acceleration of 2kg and 4kg masses, where it is given that 2kg mass does not slide on 4kg mass for the figure shown. The external force F acting on the mass 2kg at an angle θ=37∘. (Take g=10m/s2)
A
aA=aB=43m/s2
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B
aA=aB=83m/s2
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C
aA=aB=34m/s2
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D
aA=aB=103m/s2
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Solution
The correct option is BaA=aB=83m/s2 The FBDs of the masses are as shown
from the FBD we have N1=Fsin37∘+2g=(3F5+20)N
As per the given condition i.e. mass 2kg will not slide on the mass 4kg, we have
Limiting friction fmax=μN1=0.5(3F5+20)N
Also, Horizontal applied force≤fmax ⇒Fcos37∘≤0.5(3F5+20) ⇒4F5≤0.5(3F5+20) ⇒(4F5−3F10)≤10 ⇒F≤20N
Thus, the maximum value of applied external force can be Fmax=20N
∴ common acceleration of the masses is ac=Fcos37∘mA+mB=20×0.86=166=83m/s2