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An object of mass m is tied to a string of length L and a variable horizontal force is applied on it which starts at zero and gradually increases until the string makes an angel theta with the vertical. Work done by the force F is

  1. m g L left parenthesis 1 minus sin invisible function application theta right parenthesis    
  2. m g L    
  3. m g L left parenthesis 1 minus cos invisible function application theta right parenthesis    
  4. m g L left parenthesis 1 plus cos invisible function application theta right parenthesis    

The correct answer is: m g L left parenthesis 1 minus cos invisible function application theta right parenthesis


    W equals increment K or W subscript T end subscript plus W subscript g end subscript plus W subscript F end subscript equals 0
    (Since, change in kinetic energy is zero)

    Here, W subscript T end subscript equals work done by tension = 0
    W subscript g end subscript equals work done by fore of gravity
    equals negative m g h
    equals negative m g L left parenthesis 1 minus cos invisible function application theta right parenthesis
    therefore blank W subscript F end subscript equals negative W subscript g end subscript equals m g L left parenthesis 1 minus cos invisible function application theta right parenthesis

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