Question:
The radius of gyration of a regular solid cylinder of radius $R$ about its axis is
The radius of gyration of a regular solid cylinder of radius $R$ about its axis is
Show Hint
The radius of gyration is a measure of how mass is distributed around the axis of rotation.
Updated On: Apr 7, 2026
- $\frac{R}{2}$
- $R$
- $\frac{R}{\sqrt{2}}$
- $2R$
$\frac{R}{4}$
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: The moment of inertia of a solid cylinder about its central axis is: \[ I = \frac{1}{2} M R^2 \] Step 2: The radius of gyration $K$ is related to the moment of inertia by: \[ I = M K^2 \] Step 3: Equating both expressions: \[ M K^2 = \frac{1}{2} M R^2 \] \[ K^2 = \frac{R^2}{2} \] \[ K = \frac{R}{\sqrt{2}} \] Step 4: Therefore, the correct answer is (C).
Was this answer helpful?
0
0
Top KEAM Physics Questions
- A body oscillates with SHM according to the equation (in SI units), $x = 5 cos \left(2\pi t +\frac{\pi}{4}\right) .$ Its instantaneous displacement at $t = 1$ second is
Kepler's second law (law of areas) of planetary motion leads to law of conservation of
- Two capillary tubes A and B of diameter $1\, mm$ and $2\, mm$ respectively are dipped vertically in a liquid. If the capillary rise in A is 6 cm, then the capillary rise in B is
- In the circuit given in figure, 1 and 2 are ammeters. Just after key K is pressed to complete the circuit, the reading will be
- A plate has a length $ 5\pm 0.1\text{ }cm $ and breadth $ 2\pm 0.01\text{ }cm $ . Then the area of the plate is:
View More Questions
Top KEAM Rotational motion Questions
- From a circular ring of mass $M$ and radius $R$, an arc corresponding to a $ {{90}^{o}} $ sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is $k$ times $ M{{R}^{2}} $ . Then the value of $k$ is
- The propulsion of a rocket is based on the principle of conservation of
- Two persons stand at the edges of a rotating circular platform at diametrically opposite points. If they start moving towards each other at uniform velocity, then its
- A solid metal cylinder A and a hollow metal cylinder B have same mass but their radii are in the ratio 2: 1. Then the ratio of their respective moments of inertia about their own axis is
- For a smoothly running analog clock, the ratio of the angular velocity of the minute hand to the angular velocity of the hour hand is
View More Questions
Top KEAM Questions
- i.$\quad$ They help in respiration ii.$\quad$ They help in cell wall formation iii.$\quad$ They help in DNA replication iv. $\quad$They increase surface area of plasma membrane Which of the following prokaryotic structures has all the above roles?
- A body oscillates with SHM according to the equation (in SI units), $x = 5 cos \left(2\pi t +\frac{\pi}{4}\right) .$ Its instantaneous displacement at $t = 1$ second is
- The pH of a solution obtained by mixing 60 mL of 0.1 M BaOH solution at 40m of 0.15m HCI solution is
Kepler's second law (law of areas) of planetary motion leads to law of conservation of
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
View More Questions