Question

(i) Calculate the loss in time in a day of a pendulum clock having a time period of 2s at 15degree celsius, when the temperature rises to 35degree celsius. (coefficient of linear expansion= 2 x 1/100000degree celsius to power -1)

(ii) An iron cube of density 7.6 g/cubic cm has side of 5cm. Calculate the net force acting on the metal cube in alcohol of density 0.8g/cubic cm.

Answer 1

1.
                 T = 2 π √ (L/g)
       For small changes in L,  we can write :
             ΔT/T = 1/2 ΔL / L
           T = 2 s        ΔL = α ΔTemp L

               ΔT = 1/2 * T * α * ΔTemp
                ΔT = 1/2 * 2 * 2 * 10⁻⁵ * (35-15) = 4 * 10⁻⁴ Sec

             change is 0.4 milliseconds
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2)
    net Force =  weight of the cube - buoyancy force
                = 7.6 * 5³ * 9.81  N  -   0.8 * 5³ * 9.81 N
               = 1667.7  Newtons
     the direction of the net force is downwards