
A rigid body rotates about a fixed axis with variable angular velocity equal to at where and are constants. The angle through which it rotates before it comes to rest is:
(A)
(B)
(C)
(D)
Answer
475.2k+ views
Hint: Here, using the angular velocity formula, which is the angle per unit time, the angle through which the rigid body rotates before it comes to rest is computed. The angular velocity is zero at rest, so we will calculate the time and put it in the angle equation.
Complete Step-by-Step Solution:
Let us suppose the angle through which it rotates be
According to the question,
The angular velocity is given as
Now, if the body is at rest, the angular velocity of such a body is zero, i.e.,
We can now equate the value of angular velocity such that
Upon solving, we get
Also, we know that angular velocity is also measured as angle per unit time, therefore,
Rearranging the terms, we get
Now, we will integrate both the sides
Upon further solving, we get
Now, let us integrate the above expression
Let us simplify and get the final answer
Hence, the correct option is (B.)
Additional Information: Angular velocity is the quantity of a vector and is described as the angular displacement change rate that specifies the object's angular velocity or rotational velocity and the axis around which the object is rotating. At a given period of time, the amount of change in the angular displacement of the particle is called angular velocity. The angular velocity vector's track is vertical to the rotation plane, in a direction usually indicated by the right-hand rule.
Note: In the above question, we have found out the angle by integrating the equation of between the limits to . We could have also landed to the same result by putting the value of in the equation after integrating it.
Complete Step-by-Step Solution:
Let us suppose the angle through which it rotates be
According to the question,
The angular velocity is given as
Now, if the body is at rest, the angular velocity of such a body is zero, i.e.,
We can now equate the value of angular velocity such that
Upon solving, we get
Also, we know that angular velocity is also measured as angle per unit time, therefore,
Rearranging the terms, we get
Now, we will integrate both the sides
Upon further solving, we get
Now, let us integrate the above expression
Let us simplify and get the final answer
Hence, the correct option is (B.)
Additional Information: Angular velocity is the quantity of a vector and is described as the angular displacement change rate that specifies the object's angular velocity or rotational velocity and the axis around which the object is rotating. At a given period of time, the amount of change in the angular displacement of the particle is called angular velocity. The angular velocity vector's track is vertical to the rotation plane, in a direction usually indicated by the right-hand rule.
Note: In the above question, we have found out the angle by integrating the equation of
Latest Vedantu courses for you
Grade 11 Science PCM | CBSE | SCHOOL | English
CBSE (2025-26)
School Full course for CBSE students
₹41,848 per year
Recently Updated Pages
Master Class 11 Business Studies: Engaging Questions & Answers for Success

Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 Computer Science: Engaging Questions & Answers for Success

Master Class 11 Maths: Engaging Questions & Answers for Success

Master Class 11 English: Engaging Questions & Answers for Success

Trending doubts
Which one is a true fish A Jellyfish B Starfish C Dogfish class 11 biology CBSE

The flightless birds Rhea Kiwi and Emu respectively class 11 biology CBSE

Difference Between Prokaryotic Cells and Eukaryotic Cells

1 ton equals to A 100 kg B 1000 kg C 10 kg D 10000 class 11 physics CBSE

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

1 Quintal is equal to a 110 kg b 10 kg c 100kg d 1000 class 11 physics CBSE
