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Q.

A solid uniform cylinder is gently released on an inclined surface AB whose angle of inclination with horizontal can be varied. If coefficient of static friction between the cylinder and the inclined surface AB is 133, The maximum possible linear acceleration of the centre of mass of the cylinder for pure rolling, is (Take g = 10 m/s2)

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a

3.33 m/s2

b

5 m/s2

c

2.67 m/s2

d

4.33 m/s2

answer is A.

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Detailed Solution

For pure rolling down the inclined plane, maximum possible angle of inclination is given by, tan θmax  =  μ 1+mR2ICFor solid cylinder,tan θmax  = 133   1+mR212  mR2 =  13⇒θmax  =  300 ∴    amax  =  g  sin θmax 1+ ICmR2  =  10 ×  sin  3001+ 12mR2mR2    m/s2⇒   amax  = 103  m/s2  =  3.33   m/s2
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