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Question

If the system shown in the figure is at rest initially, find the common acceleration of the two block system?
(Take g=10 m/s2)


A
2 m/s2,in +ve x-direction
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B
2 m/s2,in -ve x-direction
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C
3 m/s2,in -ve x-direction
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D
3 m/s2,in +ve x-direction
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Solution

The correct option is B 2 m/s2,in -ve x-direction
The FBDs of the blocks are as shown


From the FBDs we have
N1=10g=100 N
N2=N1+20g=100+200=300 N
f1 max=μN1=1×100=100 N
f2 max=μN2=0

Now, assuming that the blocks moves together in ve x-direction with common acceleration ac
common acceleration ac=60mA+mB=6030=2 m/s2

Again, from the FBD of block B we have
f=mBac=20×2=40 N
Since, 40 N<100 N i.e. f<fmax, means our assumption is right.

Hence, both the block will move together in ve x-direction with common acceleration ac=2 m/s2

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