$\Delta SE = T \Delta A$
$=0.075\left( A _{ f }- A _{1}\right)$
$A _{ i }=4 \pi r ^{2}$
$A _{ t }=4 \pi r _{0}^{2} \times 64$
By volume conservation
$\frac{4}{3} \pi r ^{3}=64 \cdot \frac{4}{3} \pi r_{0}^{3}$
$I _{0}=\frac{ r }{4}$
$A _{ f }=4 \pi\left(\frac{ r }{4}\right)^{2} \cdot 64=16 \pi r ^{2}$
$\Delta SE =0.075\left(16 \pi r ^{2}-4 \pi r ^{2}\right)$
$=0.075\left(12 \pi(0.01)^{2}\right)$
$=2.8 \times 10^{-4}\,J$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$1.$ Which of the following statement regarding the angular speed about the istantaneous axis (passing through the centre of mass) is correct?
$(A)$ It is $\sqrt{2} \omega$ for boht the cases
$(B)$ it is $\omega$ for case $(a)$; and $\frac{w}{\sqrt{2}}$ for case $(b)$.
$(C)$ It is $\omega$ for case $(a)$; and $\sqrt{2} \omega$ for case $(b)$.
$(D)$ It is $\omega$ for both the cases
$2.$ Which of the following statements about the instantaneous axis (passing through the centre of mass) is correct?
$(A)$ It is vertical for both the cases $(a)$ and $(b)$.
$(B)$ It is verticle for case $(a)$; and is at $45^{\circ}$ to the $x-z$ plane and lies in the plane of the disc for case $(b)$
$(C)$ It is horizontal ofr case $(a)$; and is at $45^{\circ}$ to the $x - z$ plane and is normal to the plane of the disc for case $(b)$.
$(D)$ It is vertical of case $(a)$; and is at $45^{\circ}$ to the $x - z$ plane and is normal to the plane of the disc for case $(b)$.
Give the answer question $1$ and $2.$
