A hollow sphere of radius R and mass m is ful | vedclass

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(C) The total mass of the system is $M = m + m = 2m$. Since the sphere is hollow and filled with water,the moment of inertia of the shell is $I_{shell

Vedclass · Accepted Answer

Angular momentum of the sphere about a fixed point on ground is $\frac{8}{3} mvR$

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(C) The total mass of the system is $M = m + m = 2m$. Since the sphere is hollow and filled with water,the moment of inertia of the shell is $I_{shell} = \frac{2}{3} m R^2$. Assuming the water behaves as a rigid body rotating with the shell,the total moment of inertia is $I = I_{shell} + I_{water} = \frac{2}{3} m R^2 + 0$ (assuming water is non-viscous and does not rotate,but in standard physics problems of this type,we treat the system as a rigid body with $I = \frac{2}{3} m R^2$). For pure rolling,$\omega = \frac{v}{R}$. The angular momentum about a point on the ground is $L = I_{cm} \omega + M v R$. Substituting the values: $L = (\frac{2}{3} m R^2) 	imes (\frac{v}{R}) + (2m) v R$. $L = \frac{2}{3} m v R + 2 m v R = \frac{8}{3} m v R$.

$(a)$ $\frac{mg}{4} < F < \frac{mg}{2}$	$(i)$ Cube will move up
$(b)$ $F > \frac{mg}{2}$	$(ii)$ Cube will not exhibit motion
$(c)$ $F > mg$	$(iii)$ Cube will begin to rotate about $A$
$(d)$ $F = \frac{mg}{4}$	$(iv)$ Normal reaction effectively at $a/3$ from $A$,no motion

$A$ hollow sphere of radius $R$ and mass $m$ is fully filled with water of mass $m$. It is rolled down a horizontal plane such that its centre of mass moves with a velocity $v$. If it purely rolls,which of the following statements is correct?

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