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Physics

Mechanics

Easy

Question

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

$1.2 \times 10^{- 2} J$
$2.4 \times 10^{- 2} J$
$3.6 \times 10^{- 2} J$
$4.8 \times 10^{- 2} J$

The correct answer is: $2.4 cross times 10 to the power of negative 2 end exponent J$

$K. E. equals 1 half open parentheses 2 over 5 close parentheses m v squared not stretchy rightwards double arrow K. E. equals 2 over 10 m v squared table attributes columnalign left columnspacing 1em rowspacing 4 pt end attributes row cell straight capital delta straight K times straight E. equals straight K times straight E subscript 2 minus straight K times straight E subscript.1 end subscript equals 2 over 10 m open square brackets v subscript 2 superscript 2 minus v subscript 1 superscript 2 close square brackets end cell row cell table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em rowspacing 3 pt end attributes row cell v space of 1em end cell cell equals 10 minus t equals 0 straight capital delta K. E. equals 2 over 10 m open square brackets r squared omega subscript 2 superscript 2 minus r squared omega subscript 1 superscript 2 close square brackets end cell row blank cell equals 2 over 10 cross times 1 open square brackets open parentheses 1 over 10 close parentheses squared close square brackets open square brackets 4 squared minus 2 squared close square brackets equals 2.4 cross times 10 to the power of negative 2 end exponent straight J end cell end table end cell end table$

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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

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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$text A composite rod comprising two rods of mass end text straight m text and end text 2 straight m text and each of length end text l equals 1 straight m text as shown in the end text text figure. Assume end text omega equals 10 rad divided by straight s text and end text straight m equals 1 kg comma text the end text KE text of the rotating composite rod is end text$

$text A composite rod comprising two rods of mass end text straight m text and end text 2 straight m text and each of length end text l equals 1 straight m text as shown in the end text text figure. Assume end text omega equals 10 rad divided by straight s text and end text straight m equals 1 kg comma text the end text KE text of the rotating composite rod is end text$

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$text A man stands on a rotating platform with his arms stretched holding a end text 5 kg text weight in each end text text hand. The angular speed of the platform is 1.2revs end text to the power of negative 1 end exponent text . The moment of inertia of the man together end text text with the platform may be taken to be constant and equal to end text 6 kgm squared text . If the man brings his arms end text c l o s e space t o space h i s space c h e s t space w i t h space t h e space d i s tan c e space n space e a c h space w e i g h t space f r o m space t h e space a x i s space c h a n g i n g space f r o m space 100 space c m space t o space 20 c m. space T h e space n e w space a n g u l a r space s p e e d space o f space t h e space p l a t f o r m space i s$

$text A man stands on a rotating platform with his arms stretched holding a end text 5 kg text weight in each end text text hand. The angular speed of the platform is 1.2revs end text to the power of negative 1 end exponent text . The moment of inertia of the man together end text text with the platform may be taken to be constant and equal to end text 6 kgm squared text . If the man brings his arms end text c l o s e space t o space h i s space c h e s t space w i t h space t h e space d i s tan c e space n space e a c h space w e i g h t space f r o m space t h e space a x i s space c h a n g i n g space f r o m space 100 space c m space t o space 20 c m. space T h e space n e w space a n g u l a r space s p e e d space o f space t h e space p l a t f o r m space i s$

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$text Two discs of moments of inertia end text I subscript 1 text and end text I subscript 2 text about their respective axes, rotating with angular end text text frequencies, end text omega subscript 1 text and end text omega subscript 2 text respectively, are brought into contact face to face with their axes of end text text rotation coincident. The angular frequency of the composite disc will be A end text$

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$text A solid cylinder of mass end text 20 kg text and radius end text 20 cm text rotates about its axis with a angular speed end text 100 text rad end text s to the power of negative 1 end exponent. text The angular momentum of the cylinder about its axis is end text$

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$text A circular platform is mounted on a vertical frictionless axle. Its radius is end text r equals 2 m text and its moment end text text of inertia end text straight I equals 200 kgm squared text . It is initially at rest. A end text 70 kg text man stands on the edge of the platform and end text text begins to walk along the edge at speed end text v subscript 0 equals 1 ms to the power of negative 1 end exponent text relative to the ground. The angular velocity end text text of the platform is end text$

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