Rotational Motion

JEE Main level, single correct, medium

226 of 280

Question 226 of 280

A cubical block of side 30cm30cm is moving with velocity 2ms−12m{s}^{-1} on a smooth horizontal surface. The surface has a bump at a point OO as shown in the figure. The angular velocity (in rad/s) of the block immediately after it hits the bump, is :

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Answer: (B) 5.0

Conservation of angular momentum about point OO,
Lbefore=Lafter{L}_{before}={L}_{after}
⇒mvR=Iω\Rightarrow mvR=I\omega
⇒ω=m×2×[a2]m[a26+(a2)2]\Rightarrow \omega =\dfrac{m\times 2\times \left[\dfrac{a}{2}\right]}{m\left[\dfrac{{a}^{2}}{6}+{\left(\dfrac{a}{\sqrt{2}}\right)}^{2}\right]}
⇒ω=128a=32×0.3=102=5\Rightarrow \omega =\dfrac{12}{8a}=\dfrac{3}{2\times 0.3}=\dfrac{10}{2}=5 rads−1rad{s}^{-1}

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