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

Question

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

Infinity Learn · Accepted Answer

$$1$$. Given Side of block  $$a=30$$ $$cm=0.3$$ mVelocity  $$v=2$$ $$m/sBefore$$ hitting point O ,We know angular momentum $$L=mvr=mva2Also$$, after hitting point O, $$L=I$$ω$$2$$. Using conservation of angular momentum,  $$mva2=I$$ω$$3$$. Moment of inertia (I) of cubical block about one edge is given $$byI=ma26+a22$$ ∴ω$$=m.2a2ma26+a22$$ ⇒ω$$=128a=32$$×$$0.3=102=5$$ $$rad/$$$$sec$$ Therefore, the correct answer is (B).

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

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