A solid sphere of mass m = 1 kg and radius R = 10 cm is being wrapped by N turns of a massless wire, is kept on a rough inclined plane. If the wire carries a current i, the sphere remains in equilibri

Question

A solid sphere of mass m = 1 kg and radius R = 10 cm is being wrapped by N turns of a massless wire, is kept on a rough inclined plane. If the wire carries a current i, the sphere remains in equilibrium in a horizontal magnetic field B . If B is suddenly reversed, find the angular acceleration of the sphere. If answer is n × 100 rad / s 2 . Write the value of n. (Given θ = 3 7 ∘ )

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Ans (3.00)

m = 1 kg, R = 10 cm. Initially $τ_{m g} = τ_{B}$ (torques balance).

Now if we reverse direction of current: $τ_{n e t} = 2 τ_{m g}$

$2 \times m g sin θ \times R = (\frac{2}{5} m R^{2}) α$

$α = \frac{5 g s i n θ}{R} = \frac{5 \times 10 \times 3}{5 \times 10 \times 1 0 ^{- 2}} = 300$

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