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A disc of radius r is made of a material of negligible resistance and can rotate about a horizontal shaft. A smaller disc of radius is $ρ$ fixed onto the same shaft and has a massless cord wrapped around it, which is attached to a small object of mass m as shown. Two ends of a resistor of resistance R are connected to the perimeter of the disc and to the shaft by wiping contacts. The system is then placed into a uniform horizontal magnetic field B and mass m is released. Find the constant angular velocity (in rad/s) with which the disc will rotate after a certain time. If your answer is $ω$ given value of $\frac{ω}{20}$ . $(D a t a : r = 10 c m, ρ = 2 c m, R = 0.01 Ω, B = 0.2 T, m = 50 g)$

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Detailed Solution

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$V = \frac{B r^{2} ω}{2}; I = \frac{V}{R} = \frac{B r^{2} ω}{2 R}; \frac{B^{2} r^{3} ω}{2 R} . \frac{r}{2} - m g ρ = 0; ω = \frac{4 m g ρ R}{B^{2} r^{4}} = 100 s^{- 1}$

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A disc of radius r is made of a material of negligible resistance and can rotate about a horizontal shaft. A smaller disc of radius is ρ fixed onto the same shaft and has a massless cord wrapped around it, which is attached to a small object of mass m as shown. Two ends of a resistor of resistance R are connected to the perimeter of the disc and to the shaft by wiping contacts. The system is then placed into a uniform horizontal magnetic field B and mass m is released. Find the constant angular velocity (in rad/s) with which the disc will rotate after a certain time. If your answer is ω given value of ω20. (Data: r=10cm,ρ=2cm,R=0.01Ω,B=0.2T,m=50g)