Physics-
General
Easy

Question

A body weight 8 g when placed in one pan and 18 g when placed on the other pan of a false balance. If the beam is horizontal when both the pans are empty. The true weight of the body is

  1. 13 g    
  2. 12 g    
  3. 15.5 g    
  4. 15 g    

The correct answer is: 12 g


    Let the mass of first and second pan be m1 and m2, respectively and their respective distance from the pivot be L1 and L2.

    Let the true weight of the body be M.

    As the beam is horizontal when both the pans are empty, thus net torque about the pivot is zero.
      m1gL1m2gL2=0
    We get  m1L1=m2L2      ....(1)
    The body weighs 8g in first pan.
      (M+m1)gL1=(8+m2)gL2
    Or   ML1=8L2    ....(2)        (Using (1))
    The body weighs 18g in second pan.
      (18+m1)gL1=(M+m2)gL2
    Or   18L1=ML2    ....(3)        (Using (1))
    Dividing equation (2) and (3) we get  18M=M8
    Or  M2=8×18=144
      M=12 g 

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