# (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.

1
by samharsh

2015-02-12T14:17:43+05:30

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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