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Q.

A solid sphere of mass 1 kg and radius 1 m rolls without slipping on a fixed inclined plane with an angle of inclination 𝜃 = 30° from the horizontal. Two forces of magnitude 1 N each, parallel to the incline, act on the sphere, both at distance 𝑟 = 0.5 m from the center of the sphere, as shown in the figure. The acceleration of the sphere down the plane is ____ 𝑚𝑠 -2. (Take 𝑔 = 10 𝑚𝑠-2 .)

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answer is 2.86.

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Detailed Solution

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Taking torque about contact point.
τ=mgRsin30+1×1
 taking  is positive 
51=75mR2αα=207rad/s2 So, acm=αR=207m/s2acm=2.86m/s2

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