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A body having moment of inertia about its axis of rotation equal to 3 kg-m2 is rotating with angular velocity equal to 3 rad/s. Kinetic energy of this rotating body is the same as that of body of mass 27 kg moving with a speed of
- a)1.0 m/s
- b)0.5 m/s
- c)1.5 m/s
- d)2.0 m/s
Correct answer is option 'A'. Can you explain this answer?
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A body having moment of inertia about its axis of rotation equal to 3 ...
The kinetic energy of a rotating body can be calculated using the formula:
K.E. = 1/2 * I * ω²,
where K.E. is the kinetic energy, I is the moment of inertia, and ω is the angular velocity.
In this case, the moment of inertia is given as 3 kg-m² and the angular velocity is given as 3 rad/s. We can substitute these values into the formula to find the kinetic energy of the rotating body.
K.E. = 1/2 * 3 kg-m² * (3 rad/s)²
= 1/2 * 3 kg-m² * 9 rad²/s²
= 1/2 * 27 kg-m²/s²
= 13.5 J
To find the speed of a body of mass 27 kg that has the same kinetic energy, we can use the formula:
K.E. = 1/2 * m * v²,
where m is the mass and v is the speed.
Substituting the given values of K.E. and mass into the formula, we can solve for v.
13.5 J = 1/2 * 27 kg * v²
v² = (13.5 J) / (1/2 * 27 kg)
v² = 1 J/kg
v = √(1 J/kg)
Since the units of kinetic energy are joules and the units of mass are kilograms, the square root of 1 J/kg is equal to 1 m/s.
Therefore, the correct answer is option 'A', which states that the speed of the body is 1.0 m/s.
K.E. = 1/2 * I * ω²,
where K.E. is the kinetic energy, I is the moment of inertia, and ω is the angular velocity.
In this case, the moment of inertia is given as 3 kg-m² and the angular velocity is given as 3 rad/s. We can substitute these values into the formula to find the kinetic energy of the rotating body.
K.E. = 1/2 * 3 kg-m² * (3 rad/s)²
= 1/2 * 3 kg-m² * 9 rad²/s²
= 1/2 * 27 kg-m²/s²
= 13.5 J
To find the speed of a body of mass 27 kg that has the same kinetic energy, we can use the formula:
K.E. = 1/2 * m * v²,
where m is the mass and v is the speed.
Substituting the given values of K.E. and mass into the formula, we can solve for v.
13.5 J = 1/2 * 27 kg * v²
v² = (13.5 J) / (1/2 * 27 kg)
v² = 1 J/kg
v = √(1 J/kg)
Since the units of kinetic energy are joules and the units of mass are kilograms, the square root of 1 J/kg is equal to 1 m/s.
Therefore, the correct answer is option 'A', which states that the speed of the body is 1.0 m/s.
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A body having moment of inertia about its axis of rotation equal to 3 kg-m2 is rotating with angular velocity equal to 3 rad/s. Kinetic energy of this rotating body is the same as that of body of mass 27 kg moving with a speed ofa)1.0 m/sb)0.5 m/sc)1.5 m/sd)2.0 m/sCorrect answer is option 'A'. Can you explain this answer?
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A body having moment of inertia about its axis of rotation equal to 3 kg-m2 is rotating with angular velocity equal to 3 rad/s. Kinetic energy of this rotating body is the same as that of body of mass 27 kg moving with a speed ofa)1.0 m/sb)0.5 m/sc)1.5 m/sd)2.0 m/sCorrect answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A body having moment of inertia about its axis of rotation equal to 3 kg-m2 is rotating with angular velocity equal to 3 rad/s. Kinetic energy of this rotating body is the same as that of body of mass 27 kg moving with a speed ofa)1.0 m/sb)0.5 m/sc)1.5 m/sd)2.0 m/sCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body having moment of inertia about its axis of rotation equal to 3 kg-m2 is rotating with angular velocity equal to 3 rad/s. Kinetic energy of this rotating body is the same as that of body of mass 27 kg moving with a speed ofa)1.0 m/sb)0.5 m/sc)1.5 m/sd)2.0 m/sCorrect answer is option 'A'. Can you explain this answer?.
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