System of Particles and Rotational Motion - Result Question 30

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30. Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc $D_1$ has $2 kg$ mass and $0.2 m$ radius and initial angular velocity of $50 rad s^{-1}$. Disc $D_2$ has $4 kg$ mass, $0.1 m$ radius and initial angular velocity of $200 rad s^{-1}$. The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in $rad s^{-1}$ ) of the system is [NEET Kar. 2013]

======= ####30. Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc $D_1$ has $2 kg$ mass and $0.2 m$ radius and initial angular velocity of $50 rad s^{-1}$. Disc $D_2$ has $4 kg$ mass, $0.1 m$ radius and initial angular velocity of $200 rad s^{-1}$. The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in $rad s^{-1}$ ) of the system is [NEET Kar. 2013]

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/system-of-particles-and-rotational-motion/system-of-particles-and-rotational-motion—result-question-30.md (a) 40

(b) 60

(c) 100

(d) 120

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Answer:

Correct Answer: 30. (c)

Solution:

(c) Given: $m_1=2 kg$

$m_2=4 kg$

$r_1=0.2 m$

$r_2=0.1 m$

$\omega_1=50 rad s^{-1}$

$\omega_2=200 rad s^{-1}$

As, angular momentum,

$I_1 \omega_1+I_2 \omega_2=(I_1+I_2) \omega_1$

$\therefore \omega_f=\frac{I_1 \omega_1+I_2 \omega_2}{I_1+I_2}=\frac{\frac{1}{2} m_1 r_1^{2} \omega_1+\frac{1}{2} m_2 r_2^{2} \omega_2}{\frac{1}{2} m_1 r_1^{2}+\frac{1}{2} m_2 r_2^{2}}$

By putting the value of $m_1, m_2, r_1, r_2$ and solving we get $=100 rad s^{-1}$