Question 339: Centre of Mass and Rotational Motion

Question

A cubical block of side 30 cm is moving with velocity 2 ms
−1
on a smooth horizontal surface. The surface has a bump at a point O as shown in figure. The angular
velocity (in rad/s) of the block immediately after it hits the bump, is :
![](https://app-content.cdn.examgoal.net/fly/@width/image/1l80yuzar/6f5c31d9-2452-482f-85cd-67343217c6f9/acec0830-33cf-11ed-bcbd-5353ee2ab2b1/file-1l80yuzas.png?format=png)

Accepted Answer

Before hitting point 0,
angular moment = mv $ 	imes $ ${a \over 2}$
After hitting point 0,
Angular momentum  = ${m I}\omega $
$ 	herefore $    ${m I}\omega $ = ${{mva} \over 2}$
$ \Rightarrow $   $\omega $ = ${{mva} \over {2{m I}}}$
${m I}$ = moment of inertia about edge,
=   ${{m{a^2}} \over 6} + m{\left( {{a \over {\sqrt 2 }}} ight)^2}$
=   ${{m{a^2}} \over 6} + {{m{a^2}} \over 2}$
=   ${{2m{a^2}} \over 3}$
$ 	herefore $   $\omega $ = ${{mva} \over {2 	imes {{2m{a^2}} \over 3}}}$ = ${{3v} \over {4a}}$ = ${{3 	imes 2} \over {4 	imes 0.3}}$ = 5 rad/s

Answer

5.0

Answer

6.7

Answer

9.4

Answer

13.3

Centre of Mass and Rotational Motion

A cubical block of side 30 cm is moving with velocity 2 ms −1 on a smooth horizontal surface. The surface has a bump at a point O as shown in figure. The angular velocity (in rad/s) of the block immediately after it hits the bump, is :

Choose the correct answer: