Consider the situation shown in figure in which a book `'A'` of mass `2 kg` is placed over a block `'B'` of mass `4 kg`. The combination of the placed on a inclined plane of inclination `37 ^(@)` with horizontal. The coefficient of friction between blocks `B` and inclined plane is `mu_(2)` and in between the two bolcks is `mu_(1)`, The system is released from rest.
( Take `g=10m//sec^(2))`

If `mu_(1)=0.5, mu_(2)=0.5`, then:

Options

A. Both blocks will move but with different accelerations
B. Both blocks will move together
C. Only block `A` will move
D. Onlyd block `B` will have

Answer

B

Explanation

Here, `mu_(1)=mu_(2)=0.5lt tan 37^(@)=0.75`
i.e., `mu lt tan theta`
`therefore` both block will move

Let both blocks move together with acceleration `'a'`
`therefore 12-f_(1)=2a(24+f_(1)-24=4a)/(12=6a)`
`a=2m//sec^(2)rArrf_(1)=12-2xx2=8N`
i.e., `f_(1)` required `=f_(1)` max. `therefore` both will move together