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Engineering
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A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc

Option 1)

remains unchanged

Option 2)

continuously decreases

Option 3)

continuously increases

Option 4)

first increases and then decreases

As we learnt in Rotational angular momentum -   - wherein = Moment of inertia about fixed axis of rotation = angular velocity of rotation      First - increases (towards the centre) then - decreases (away from the centre) We know that  Ans. 4 Option 1) remains unchanged This is an incorrect option. Option 2) continuously decreases This is an incorrect option. Option 3) continuously...
Engineering
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A mass m hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass m and radius R . Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass m , if the string does not slip on the pulley, is

Option 1)

\frac{3}{2}g

Option 2)

g

Option 3)

\frac{2}{3}g

Option 4)

\frac{g}{3}

As we learnt in Rolling of a body on an inclined plane - - wherein K=Radius of gyration = Angle of inclination       Option 1) This is an incorrect option. Option 2) This is an incorrect option. Option 3) This is the correct option. Option 4) This is an incorrect option.
Engineering
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A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

Option 1)

less than 3

Option 2)

more than 3 but less than 6

Option 3)

more than 6 but less than 9

Option 4)

more than 9

As we learnt in Analogue of second law of motion for pure rotation - - wherein Torque equation can be applied only about two points (i) centre of motion. (ii) point which has zero velocity/acceleration.      is zero at   t = 6 sec    No. of revolution  less than 6 Ans. 4 Option 1) less than 3 This an incorrect option. Option 2) more than 3 but less than 6 This is the correct...
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