A solid sphere of mass 2 ,kg and radius 1 ,m | vedclass

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(B) Given: Mass $M = 2 \,kg$, Radius $R = 1 \,m$, Final angular velocity $\omega = 10 \,rad/s$, Time $t = 2 \,s$, Initial angular velocity $\omega_0 =

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$4$

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(B) Given: Mass $M = 2 \,kg$, Radius $R = 1 \,m$, Final angular velocity $\omega = 10 \,rad/s$, Time $t = 2 \,s$, Initial angular velocity $\omega_0 = 0$.First, calculate the angular acceleration $\alpha$ using $\omega = \omega_0 + \alpha t$:$10 = 0 + \alpha(2) \implies \alpha = 5 \,rad/s^2$.The moment of inertia $I$ of a solid sphere about its axis is $I = \frac{2}{5}MR^2 = \frac{2}{5}(2)(1)^2 = 0.8 \,kg \cdot m^2$.The torque $	au$ is given by $	au = I\alpha = 0.8 	imes 5 = 4 \,N \cdot m$.Since the force $F$ is applied tangentially, $	au = F 	imes R$.Therefore, $F = \frac{	au}{R} = \frac{4 \,N \cdot m}{1 \,m} = 4 \,N$.

$A$ solid sphere of mass $2 \,kg$ and radius $1 \,m$ is free to rotate about an axis passing through its centre. $A$ constant tangential force $F$ is required to rotate the sphere with $10 \,rad/s$ in $2 \,s$ starting from rest. The value of $F$ is . . . . . . (in $\,N$)

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