A solid sphere with uniform density and radius R is rotating initially with constant angular velocity () about its diameter. After sometime during the rotation its starts loosing mass at a uniform rate, with no change in its shape. The angular velocity of

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
A solid sphere with uniform density and radius R is rotating initially with constant angular velocity ( $ω_{1}$ ) about its diameter. After sometime during the rotation its starts loosing mass at a uniform rate, with no change in its shape. The angular velocity of the sphere when its radius become R/2 is $x ω_{1}$ . The value of x is _________. [2025]

Ans.
(32)

When the sphere is of radius R, its mass is M, when radius is reduced to $\frac{R}{2}$ , mass will reduced to $\frac{M}{8}$

Angular momentum will remain conserve.

$L_{1} = L_{2} \Rightarrow I_{1} ω_{1} = I_{2} ω_{2}$

$(\frac{2}{5} M R^{2}) ω_{1} = (\frac{2}{5} (\frac{M}{8}) {(\frac{R}{2})}^{2}) ω_{2}$

$ω_{2} = 32 ω_{1}$ value of x is 32.

Want Us to Email you About Special Offers & Updates?