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Rotational Motion question

2013 · Q152
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Rotational Motion question

2013 · Q152

NEETPhysicsRotational MotionMCQ+4 / −1
Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc D1 has 2 kg mass and 0.2 m radius and initial angular velocity of 50 rad s−-−1. Disc D2 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
  1. A
    60
  2. B
    100
  3. C
    120
  4. D
    40
View written solutionFree

Correct answer: B

Given:m1 = 2 kg m2 = 4 kg
r1 = 0.2 m r2 = 0.1 m
w1 = 50 rad s–1 w2 = 200 rad s–1

As, angular momentum, I1W1 = I2W2 = Constant

Wf=I1W1+I2W2I1+I2=12m1r12w1+12m2r22w212m1r12+12m2r22{W_f} = {{{I_1}{W_1} + {I_2}{W_2}} \over {{I_1} + {I_2}}} = {{{1 \over 2}{m_1}r_1^2{w_1} + {1 \over 2}{m_2}r_2^2{w_2}} \over {{1 \over 2}{m_1}r_1^2 + {1 \over 2}{m_2}r_2^2}}Wf​=I1​+I2​I1​W1​+I2​W2​​=21​m1​r12​+21​m2​r22​21​m1​r12​w1​+21​m2​r22​w2​​

By putting the value of m1, m2, r1, r2 and solving we get = 100 rad s–1

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