Correct Answer: Option A

Explanation

     Let the original length L=xm

      ;New length =( x -3 ) m

       \(T_1\) = 5.77s; \(T_2\) = 4.60s,  

       \(T^2\) α  L

       ⇒\(T^2\) = kL  where K is constant

       ⇒ K =  \(\frac{T^2_1}{L_1} =  \frac{T^2_2}{L_2}\)

      ⇒\(\frac{5.77^2}{x}\)  = \(\frac{4.60^2}{x-3}\)

      ⇒ \(\frac{33.29}{x}\)  = \(\frac{4.60^2}{x-3}\)

      ⇒ 33.29(x-3)  = 21.16x
        
      ⇒ 33.29x - 99.87 =21.16x

      ⇒12.13x = 99.87
     
      ;x =\(\frac{99.87}{12.13}\)  = 8.23m
    
      The new length of the pendulum 
     
      =x-3 = 8.23-3
   
      =5.23m

     

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