A sphere of diameter r is cut from a sphere o | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the radius of the original sphere be $R = r$. The mass of the original sphere is $M = \rho \cdot \frac{4}{3} \pi r^3$.$A$ smaller sphere of di

Vedclass · Accepted Answer

none of these

Vedclass · Answer

(D) Let the radius of the original sphere be $R = r$. The mass of the original sphere is $M = \rho \cdot \frac{4}{3} \pi r^3$.$A$ smaller sphere of diameter $r$ is cut out,so its radius is $r' = \frac{r}{2}$.The mass of the removed sphere is $m = \rho \cdot \frac{4}{3} \pi (\frac{r}{2})^3 = \frac{M}{8}$.To maximize the distance of the center of mass of the remaining part from the original center,the smaller sphere must be cut such that its center is at the maximum possible distance from the original center,which is $d = R - r' = r - \frac{r}{2} = \frac{r}{2}$.The distance of the center of mass of the remaining part from the original center is given by $x = \frac{m \cdot d}{M - m}$.Substituting the values: $x = \frac{(\frac{M}{8}) \cdot (\frac{r}{2})}{M - \frac{M}{8}} = \frac{\frac{Mr}{16}}{\frac{7M}{8}} = \frac{Mr}{16} \cdot \frac{8}{7M} = \frac{r}{14}$.Since $\frac{r}{14}$ is not among the given options,the correct answer is 'none of these'.

$A$ sphere of diameter $r$ is cut from a sphere of radius $r$ such that the centre of mass of the remaining mass is at the maximum distance from the original centre. What is this distance?

Similar Questions

$A$ uniform circular disc has radius $r$. $A$ square portion of diagonal $r$ is cut from it. The centre of mass of the remaining disc from the centre of the disc is

$A$ uniform square plate of side $a$ has a circular hole of diameter $a$ cut out from it as shown in the figure. The centre of the hole is at the centre of the square. The centre of mass of the remaining part is:

From a circular disc of radius $R$,a square is cut out with a radius as its diagonal. The center of mass of the remaining part is at a distance (from the centre) of:

In the cube of side $a$ shown in the figure,the vector from the central point $G$ of the face $ABOD$ to the central point $H$ of the face $BEFO$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module