We have two spheres,one of which is hollow an | vedclass

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

Question

(C) The moment of inertia of a hollow sphere about its diameter is $I_{1} = \frac{2}{3} m r_{1}^{2}$.The moment of inertia of a solid sphere about its

Vedclass · Accepted Answer

$\sqrt{3}:\sqrt{5}$

Vedclass · Answer

(C) The moment of inertia of a hollow sphere about its diameter is $I_{1} = \frac{2}{3} m r_{1}^{2}$.The moment of inertia of a solid sphere about its diameter is $I_{2} = \frac{2}{5} m r_{2}^{2}$.Given that the masses and moments of inertia are identical,we have $I_{1} = I_{2}$.Substituting the formulas: $\frac{2}{3} m r_{1}^{2} = \frac{2}{5} m r_{2}^{2}$.Canceling $2m$ from both sides,we get $\frac{r_{1}^{2}}{3} = \frac{r_{2}^{2}}{5}$.Rearranging the terms,$\frac{r_{1}^{2}}{r_{2}^{2}} = \frac{3}{5}$.Taking the square root of both sides,the ratio of their radii is $r_{1} : r_{2} = \sqrt{3} : \sqrt{5}$.

We have two spheres,one of which is hollow and the other solid. They have identical masses and moments of inertia about their respective diameters. The ratio of their radii is given by

Similar Questions

Yeast is used in the production of

The major product of the following reaction is:

An object is projected with a velocity of $20 \ m/s$ making an angle of $45^\circ$ with the horizontal. The equation for the trajectory is $h = Ax - Bx^2$,where $h$ is height,$x$ is horizontal distance,and $A$ and $B$ are constants. The ratio $A : B$ is $(g = 10 \ m/s^2)$.

The ratio of most probable velocity $(u_{mp})$,average velocity $(u_{av})$,and root mean square velocity $(u_{rms})$ is .......

Vedclass Test Series

Exam Paper Generator

Online Exam Module