Question

A solid sphere and a hollow sphere of equal mass and radius are placed over a rough horizontal surface after rotating it about Its mass centre with same angular velocity ${\omega }_0$. Once the pure rolling starts (let $v_1$ and $v_2$ be the linear speeds of their centre of masses), then

• A. $v_1=v_2$
• B. $v_1>v_2$
• C. $v_1<v_2$
• D. None of these

Answer 1

Answer: (C)

$v_1<v_2$

Given,

The mass of slid sphere and a hollow sphere is equal.

Now the mass $=m$

let the linear speed of the centre of mass of solid sphere$=v_1$

the linear speed of the centre of mass of hollow sphere$=v_2$

Though mass and radius will be same of solid sphere ad a hollow sphere then,

$v=velocity=\cfrac{d}{t}\=\cfrac{distance}{time}$

Where, time will be taken more when the volume in large

$v\alpha \frac{1}{time},v=\omega r(r=radius)$

$v=velocity=frequency\times wavelength=n\lambda v\alpha n$

Frequency is less in solid sphere than a hollow sphere

$v_1<v_2$