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MHT CET20244 May 2024Evening ShiftPhysicsRotational MotionActual

A carpet of mass ' M ' made of a material is rolled along its length in the form of a cylinder of radius ' R ' and kept above the rough floor. If the carpet is unrolled without sliding to a radius ' R / 2 '. The change in potential energy is ( g = acceleration due to gravity)

Options

  1. AMgR
  2. B7 8 MgR
  3. C5 7 MgR
  4. D3 4 MgR

Correct answer

B. 7 8 MgR

Step-by-step solution

Density ( =M / V ) of carpet remains the same after it is unrolled, ₁= ₂ If M ₂ and V ₂ are mass and volume respectively of unrolled carpet, aligned & M ~V = M ₂ ~V ₂ & M ₂= M R ^2 l R ₂ l= M R ^2 l ( R ^2 4 ) l aligned M ₂= M 4 ...(i) Potential energy of rolled carpet, U ₁= MgR Potential energy of unrolled carpet, U ₂= M ₂ gR ₂= ( M 4 ) g ( R 2 )...[From(i)] Change in potential energy, aligned & U=U₁-U₂ & U=M g R- ( M 4 ) g ( R 2 ) & U= 7 8 M g R aligned

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