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A solid sphere is in rolling motion. In rolling motiona body possesses translational kinetic energy (Kt) aswell as rotational kinetic energy (Kr) simultaneously.The ratio Kt : (Kt + Kr) for the sphere is
- a)7 : 10
- b)5 : 7
- c)10 : 7
- d)2 : 5
Correct answer is option 'B'. Can you explain this answer?
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Explanation:
In rolling motion, a body possesses both translational kinetic energy (Kt) and rotational kinetic energy (Kr) simultaneously. The ratio Kt : (Kt + Kr) for a solid sphere can be determined by considering the expressions for these energies.
Translational Kinetic Energy (Kt):
The translational kinetic energy of an object is given by the formula:
Kt = 1/2 * m * v^2
Where:
Kt = Translational kinetic energy
m = Mass of the object
v = Velocity of the object
Rotational Kinetic Energy (Kr):
The rotational kinetic energy of a rotating body is given by the formula:
Kr = 1/2 * I * ω^2
Where:
Kr = Rotational kinetic energy
I = Moment of inertia of the object
ω = Angular velocity of the object
Ratio Kt : (Kt + Kr):
To find the ratio Kt : (Kt + Kr), we need to express both Kt and Kr in terms of the same variable. In this case, we can express both energies in terms of the velocity (v) of the object.
Using the formula for translational kinetic energy, we have:
Kt = 1/2 * m * v^2
Using the formula for rotational kinetic energy, we can express ω in terms of v:
ω = v / r
Where:
r = Radius of the sphere
Substituting this value of ω in the formula for rotational kinetic energy, we have:
Kr = 1/2 * I * (v/r)^2
Since the moment of inertia (I) of a solid sphere is given by:
I = 2/5 * m * r^2
Substituting this value of I in the formula for rotational kinetic energy, we have:
Kr = 1/2 * (2/5 * m * r^2) * (v/r)^2
= 1/5 * m * v^2
Now, we can determine the ratio Kt : (Kt + Kr) by substituting the values of Kt and Kr:
Kt : (Kt + Kr) = (1/2 * m * v^2) : (1/2 * m * v^2 + 1/5 * m * v^2)
= (1/2) : (1/2 + 1/5)
= (1/2) : (7/10)
= 5 : 7
Therefore, the correct answer is option 'B': 5 : 7.
In rolling motion, a body possesses both translational kinetic energy (Kt) and rotational kinetic energy (Kr) simultaneously. The ratio Kt : (Kt + Kr) for a solid sphere can be determined by considering the expressions for these energies.
Translational Kinetic Energy (Kt):
The translational kinetic energy of an object is given by the formula:
Kt = 1/2 * m * v^2
Where:
Kt = Translational kinetic energy
m = Mass of the object
v = Velocity of the object
Rotational Kinetic Energy (Kr):
The rotational kinetic energy of a rotating body is given by the formula:
Kr = 1/2 * I * ω^2
Where:
Kr = Rotational kinetic energy
I = Moment of inertia of the object
ω = Angular velocity of the object
Ratio Kt : (Kt + Kr):
To find the ratio Kt : (Kt + Kr), we need to express both Kt and Kr in terms of the same variable. In this case, we can express both energies in terms of the velocity (v) of the object.
Using the formula for translational kinetic energy, we have:
Kt = 1/2 * m * v^2
Using the formula for rotational kinetic energy, we can express ω in terms of v:
ω = v / r
Where:
r = Radius of the sphere
Substituting this value of ω in the formula for rotational kinetic energy, we have:
Kr = 1/2 * I * (v/r)^2
Since the moment of inertia (I) of a solid sphere is given by:
I = 2/5 * m * r^2
Substituting this value of I in the formula for rotational kinetic energy, we have:
Kr = 1/2 * (2/5 * m * r^2) * (v/r)^2
= 1/5 * m * v^2
Now, we can determine the ratio Kt : (Kt + Kr) by substituting the values of Kt and Kr:
Kt : (Kt + Kr) = (1/2 * m * v^2) : (1/2 * m * v^2 + 1/5 * m * v^2)
= (1/2) : (1/2 + 1/5)
= (1/2) : (7/10)
= 5 : 7
Therefore, the correct answer is option 'B': 5 : 7.
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A solid sphere is in rolling motion. In rolling motiona body possesses translational kinetic energy (Kt) aswell as rotational kinetic energy (Kr) simultaneously.The ratio Kt : (Kt + Kr) for the sphere isa)7 : 10b)5 : 7c)10 : 7d)2 : 5Correct answer is option 'B'. Can you explain this answer?
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A solid sphere is in rolling motion. In rolling motiona body possesses translational kinetic energy (Kt) aswell as rotational kinetic energy (Kr) simultaneously.The ratio Kt : (Kt + Kr) for the sphere isa)7 : 10b)5 : 7c)10 : 7d)2 : 5Correct answer is option 'B'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A solid sphere is in rolling motion. In rolling motiona body possesses translational kinetic energy (Kt) aswell as rotational kinetic energy (Kr) simultaneously.The ratio Kt : (Kt + Kr) for the sphere isa)7 : 10b)5 : 7c)10 : 7d)2 : 5Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid sphere is in rolling motion. In rolling motiona body possesses translational kinetic energy (Kt) aswell as rotational kinetic energy (Kr) simultaneously.The ratio Kt : (Kt + Kr) for the sphere isa)7 : 10b)5 : 7c)10 : 7d)2 : 5Correct answer is option 'B'. Can you explain this answer?.
A solid sphere is in rolling motion. In rolling motiona body possesses translational kinetic energy (Kt) aswell as rotational kinetic energy (Kr) simultaneously.The ratio Kt : (Kt + Kr) for the sphere isa)7 : 10b)5 : 7c)10 : 7d)2 : 5Correct answer is option 'B'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A solid sphere is in rolling motion. In rolling motiona body possesses translational kinetic energy (Kt) aswell as rotational kinetic energy (Kr) simultaneously.The ratio Kt : (Kt + Kr) for the sphere isa)7 : 10b)5 : 7c)10 : 7d)2 : 5Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid sphere is in rolling motion. In rolling motiona body possesses translational kinetic energy (Kt) aswell as rotational kinetic energy (Kr) simultaneously.The ratio Kt : (Kt + Kr) for the sphere isa)7 : 10b)5 : 7c)10 : 7d)2 : 5Correct answer is option 'B'. Can you explain this answer?.
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