Assertion (A): The moment of inertia of a ste | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The moment of inertia $(I)$ of a solid sphere about its diameter is given by the formula $I = \frac{2}{5}MR^2$, where $M$ is the mass and $R$ is t

Vedclass · Accepted Answer

$(A)$ is true but $(R)$ is wrong

Vedclass · Answer

(C) The moment of inertia $(I)$ of a solid sphere about its diameter is given by the formula $I = \frac{2}{5}MR^2$, where $M$ is the mass and $R$ is the radius of the sphere.Since the steel sphere has a higher density than the wooden sphere, for the same radius, the mass of the steel sphere is greater than that of the wooden sphere.Therefore, the moment of inertia of the steel sphere is larger than that of the wooden sphere. Thus, Assertion $(A)$ is true.However, the formula $I = \frac{2}{5}MR^2$ clearly shows that the moment of inertia depends on the mass $(M)$ of the body.Therefore, Reason $(R)$ is false.Hence, the correct option is $(C)$.

Assertion $(A)$: The moment of inertia of a steel sphere is larger than the moment of inertia of a wooden sphere of the same radius.
Reason $(R)$: Moment of inertia is independent of the mass of the body.
The correct one is:

Similar Questions

The ratio of the radius of gyration of a solid sphere of mass $M$ and radius $R$ about its own axis to the radius of gyration of a thin hollow sphere of the same mass and radius about its axis is:

Two circular loops $P$ and $Q$ of radii $r$ and $nr$ are made respectively from a uniform wire. The moment of inertia of loop $Q$ about its axis is $4$ times that of loop $P$ about its axis. The value of $n$ is:

The moment of inertia of a ring of mass $M$ and radius $R$ about an axis passing through its center and perpendicular to its plane is:

$A$ body of mass $m$ and radius of gyration $K$ has an angular momentum $L$. Then its angular velocity is

If a wheel rotating with a constant angular speed experiences a break during its motion,what happens to its radius of gyration?

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Assertion $(A)$: The moment of inertia of a steel sphere is larger than the moment of inertia of a wooden sphere of the same radius.Reason $(R)$: Moment of inertia is independent of the mass of the body.The correct one is: