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Question

Find the acceleration of block of mass m w.r.t ground if acceleration of M is b=4 m/s2. (Assume all surfaces to be smooth and string inextensible.)


A
2 m/s2
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B
3 m/s2
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C
4 m/s2
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D
1 m/s2
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Solution

The correct option is C 4 m/s2
The given system can be reframed as shown

From constrained condition and using method of intercept we have
..L1+..L2=0
ax+bcosθb=0
ax=b(1cosθ)=b(1cos60)
ax=4(112)=2 m/s2

From wedge constraint, the accelerations of the bodies along the perpendicular to the surface of contact should be equal.
ay=bsinθ=bsin60=32×4=23 m/s2
a=a2x+a2y=22+(23)2=16=4 m/s2
Thus, the net acceleration of the mass m is 4 m/s2

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