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A block P of mass m is placed on horizon...

A block P of mass m is placed on horizontal frictionless plane. A second block of same mass m is placed on it and is connected to a spring of spring constant k, the two blocks are pulled by distance A. Block Q oscillates without slipping. What is the maximum value of frictional force between the two blocks.

A

(a)`kA`

B

(b)`(kA)/(2)`

C

(c)zero

D

(d)`mu_(s)mg`

Text Solution

Verified by Experts

The correct Answer is:
B
Block Q oscillates but does not slipe on P. It mean that acceleration is same for Q and P both. There is a force of friction between the two blocks while the horizontal plane is frictinless. The spring is connected to upper block. The (P-Q) system oscilaltes with angular frequency `omega`. The spring is streactched by A.
`:. omega = sqrt((k)/(m + m)) = sqrt((k)/(2m))`
`:. ` Maximum acceleration in SHM `= omega^(2)A`
`a_(m) = (kA)/(2m)"......."(i)`
Now consider the lower block.
Let the maximum force of friction `=f_(m)`
`:. f_(m) = ma_(m) rArr f_(m) = m xx (kA)/(2m) rArr f_(m) = (kA)/(2)`
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