Question

If a Parrot starts flying upwards with an acceleration in an air tight cage, then the boy will feel the weight of the cage:

• A. Unchanged
• B. Reduced
• C. Increased
• D. Nothing can be said

Answer 1

The correct option is A Unchanged

The weight of the cage will be unchanged here.

$\frac{dP}{dr}=pg\left(r\right)g\left(r\right)=\frac{Gm\left(r\right)}{r^3}\cdot m\left(r\right)=\frac{4}{3}\pi p{r}^3⟹g\left(r\right)=\frac{4}{3}\pi pGr⟹\frac{dP}{dr}=\frac{4}{3}\pi p^{2}Gr⟹p\left(r\right)-p\left(R\right)=\frac{4}{3}\pi p^{2}G\left(\frac{R^2-r^2}{2}\right)⟹p\left(r\right)-p\left(R\right)=\frac{2}{3}\pi p^{2}G(R^2-r^2)$

Put $p\left(R\right)=0$

$⟹p\left(r\right)=\frac{2}{3}\pi p^{2}G(R^2-r^2)⟹\frac{p\left(\frac{3R}{5}\right)}{p\left(\frac{2R}{5}\right)}=\frac{1-\frac{9}{16}}{1-\frac{4}{9}}=\frac{9}{16}\times \frac{7}{5}=\frac{63}{80}⟹\frac{p\left(\frac{3R}{5}\right)}{p\left(\frac{2R}{5}\right)}=\frac{1-\frac{9}{25}}{1-\frac{4}{25}}=\frac{16}{21}$