Question

# Two blocks m1and m2, are acted upon by the forces F1 and F2 as shown in the fig. If there is no relative sliding between the blocks and the ground is smooth, find the magnitude of static friction between the blocks.Make necessary assumptions.

A

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B

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C

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D

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Solution

## The correct option is A As there is no sliding between the blocks the friction will be static. Assuming the frictional forces on m1 as f(←) and m2 as f(→), we have drawn the Free body diagram without normal reactions and weights. Referring to Free body diagram as shown in figure, we have the following equations of motion. For m1: F1 - f = m1a1 . . . . . . (i) For m2 : F2 + f = m2a2 . . . . . . (ii) Since the friction is static, a1 = a2 Substituting a1 from equation (i) a2 from equation (ii) in‘equation (iii), we have F1−fm1=F2+fm2 This gives f = m2F1−m1F2m1+m2 case(ii) Friction on m1isactinginrightwarddirection. For m1:F1+f=m1a1andform2:F2−f=m2a2 As static, a1=a2 ∴F1+fm1=F2−fm2 ⇒f=m1F2−m2F1m1+m2 ∴Magnitude of f=m2F1−m1F2m1+m2

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