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Q.

A tangential force of 10 N is acting on a circular plate of radius 50 cm such that it can rotate about an axis perpendicular to its plane passing through its center. If its moment of inertia about the given axis is $0.5 k g m^{2}$ , find the number of revolutions it makes in the first 6 seconds is

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a

$10 / π$

b

$90 / π$

c

$70 / π$

d

$20 / π$

answer is B.

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Detailed Solution

$τ = I α = R F$

$α = \frac{R F}{I}$

$α = \frac{0.5 \times 10}{0.5} = 10 r a d / s^{2}$

$then θ = \frac{1}{2} α t^{2} = \frac{1}{2} \times 10 \times 6^{2} = 180 r a d$

$when θ = 2 π N$

$N = \frac{180}{2 π} = \frac{90}{π}$

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A tangential force of 10 N is acting on a circular plate of radius 50 cm such that it can rotate about an axis perpendicular to its plane passing through its center. If its moment of inertia about the given axis is 0.5 kg m2 , find the number of revolutions it makes in the first 6 seconds is