A varying horizontal force F=at acts on a block of mass m kept on a smooth horizontal surface. An identical block is kept on the first block. The coefficient of friction between the blocks is µ. The time after which relative sliding between the blocks prevails is:

(a) 2mg/a (b) 2µmg/a (c) µmg/a (d) 2µmga

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Solution

Force Equs for 2 blocks area
at- f = mA (1)

f = mA (2)

A is the accelaration of 2 blocks before relative sliding.Solving above eqs. we get

f = at/2

Now when relative sliding starts then

f = Nk = mgµ
and f=at/2

at/2 = mgµ

or t = 2mgµ/a

So the option is (b)

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Force Equs for 2 blocks area at- f = mA ________(1) f = mA ________(2) A is the accelaration of 2 blocks before relative sliding.Solving above eqs. we get f = at/2 Now when relative sliding starts then f = Nk = mgµ and f=at/2 at/2 = mgµ or t = 2mgµ/a So the option is (b)

Force Equs for 2 blocks area
at- f = mA (1)

f = mA (2)

A is the accelaration of 2 blocks before relative sliding.Solving above eqs. we get

f = at/2

Now when relative sliding starts then

f = Nk = mgµ
and f=at/2

at/2 = mgµ

or t = 2mgµ/a

So the option is (b)