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Q.

A varying horizontal force $F = a t$ 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

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a

$\frac{2 m g}{a}$

b

$\frac{2 μ m g}{a}$

c

$\frac{μ m g}{a}$

d

$2 μ m g a$

answer is B.

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Detailed Solution

Question Image

Given
Horizontal force F=at
Coefficient of friction $= μ$

$\begin{array}{l} F o r u p p e r b l o c k : f_{s} = m a \\ F o r l o w e r b l o c k : F - f_{s} = m a \\ S o l v i n g w e g e t, \\ f_{s} = \frac{F}{2} \\ R e l a t i v e s l i d i n g s t a r t s w h e n f_{s} c r o s s t h e v a l u e f_{L .} \\ ∴ f_{s} = f_{L} \\ \Rightarrow \frac{F}{2} = μ m g \\ \Rightarrow \frac{a t}{2} = μ m g \\ \Rightarrow t = \frac{2 μ m g}{a} \end{array}$

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