Rotational Motion Question 27
Question: This question has Statement land Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements.Statement 1: When moment of inertia/of a body rotating about an axis with angular speed $ \omega $ increases, its angular momentum L is unchanged but the kinetic energy K increases if there is no torque applied on it.Statement 2: $ L=I\omega , $ kinetic energy of rotation $ =\frac{1}{2}I{{\omega }^{2}} $
[JEE ONLINE 12-05-2012]
Options:
A) Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.
B) Statement 1 is false, Statement 2 is true.
C) Statement 1 is true, Statement 2 is true. Statement 2 is correct explanation of the Statement 1.
D) Statement 1 is true, Statement 2 is false.
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] As so L increases with increase in co.
Kinetic energy depends on an angular velocity’ co’ and moment of inertia of the body I.
As L=$Iω$ so L increases with increase in co. Kinetic energy (rotational) depends on an angular velocity ω of and moment of inertia of the body I.
i.e., K.E.(rotational)= $\frac{1}{2}$ $I ω^2$
