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mechanics

Easy

Question

$space A space t h i n space minus w a l l e d space p i p e space r o l l s space a l o n g space t h e space f l o o r. space W h a t space i s space t h e space r a t i o space o f space i t s space t r a n s l a t i o n a l space k i n e t i c space e n e r g y space t o space i t s space r o t a t i o n a l space k i n e t i c space e n e r g y space a b o u t space t h e space c e n t r a l space a x i s space p a r a l l e l space t o space i t s space l e n g t h space ?$

1
3/2
2/3
4/3

The correct answer is: 1

$text The rotational kinetic energy is end text K equals 1 half I omega squared comma text where end text I equals m R squared text is its rotational inertia the centre of mas end text stack text The end text with _ below text ratio is end text K subscript text tram end text 1 end subscript over K subscript text tot end text end subscript equals fraction numerator 1 half m v subscript text com end text end subscript superscript 2 over denominator 1 half open parentheses m R squared close parentheses open parentheses v subscript text com end text end subscript divided by R close parentheses squared end fraction equals 1.00.$

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$text A copper ball of mass end text straight m equals 1 kg text with a radius of end text straight r equals 10 cm text rotates with angular velocity end text omega equals 2 rad divided by straight s text about an axis passing through its centre. The work should be performed to increases the angular velocity of rotation of the end text text ball two fold is end text$

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A solid uniform disk of mass m and radius R is pivoted about a horizontal axis through its centre and a small body of mass m is attached to the rim of the disk. If the disk is released from rest with the small body, initially at the same level as the centre, the angular velocity when the small body reaches the lowest point of the disk is

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A loop and a disc have same mass and roll without slipping with the same linear velocity . If the total kinetic energy of the loop is 8J, the kinetic energy of the disc must be

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$text The moment of inertia of a body about a given axis is end text 1.2 kgm squared text . Initially the body is at rest. In order to end text text produce a rotational end text KE text of end text 1500 text joule an angular acceleration of end text 25 rad divided by straight s squared text must be applied about the axis for a duration end text o f$

$text The moment of inertia of a body about a given axis is end text 1.2 kgm squared text . Initially the body is at rest. In order to end text text produce a rotational end text KE text of end text 1500 text joule an angular acceleration of end text 25 rad divided by straight s squared text must be applied about the axis for a duration end text o f$

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