M.I. of solid sphere, is
A. $$\frac{2}{3}{\text{M}}{{\text{r}}^2}$$
B. $$\frac{2}{5}{\text{M}}{{\text{r}}^2}$$
C. $${\text{M}}{{\text{r}}^2}$$
D. $$\frac{1}{2}{\text{M}}{{\text{r}}^2}$$
Answer: Option B
Solution(By Examveda Team)
The moment of inertia (II) of a solid sphere can be calculated using the formula:I=$$\frac{2}{5}{\text{M}}{{\text{r}}^2}$$
Where:
I is the moment of inertia.
M is the mass of the sphere.
r is the radius of the sphere.
In this formula, we can see that the moment of inertia depends on both the mass of the sphere (MM) and the square of its radius (r2). The factor $$\frac{2}{5}$$ is a constant that relates to the distribution of mass within a solid sphere. This formula is specific to solid spheres and is derived from the integration of infinitesimal mass elements over the entire volume of the sphere.
So, the moment of inertia for a solid sphere is $$\frac{2}{5}$$ times the product of its mass and the square of its radius. This property is important in physics and engineering, especially when analyzing the rotational motion of objects.
This Question Belongs to Civil Engineering >> Applied Mechanics And Graphic Statics
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Comments ( 2 )
In case of S.H.M. the period of oscillation (T), is given by
A. $${\text{T}} = \frac{{2\omega }}{{{\pi ^2}}}$$
B. $${\text{T}} = \frac{{2\pi }}{\omega }$$
C. $${\text{T}} = \frac{2}{\omega }$$
D. $${\text{T}} = \frac{\pi }{{2\omega }}$$
The angular speed of a car taking a circular turn of radius 100 m at 36 km/hr will be
A. 0.1 rad/sec
B. 1 rad/sec
C. 10 rad/sec
D. 100 rad/sec
A body is said to move with Simple Harmonic Motion if its acceleration, is
A. Always directed away from the centre, the point of reference
B. Proportional to the square of the distance from the point of reference
C. Proportional to the distance from the point of reference and directed towards it
D. Inversely proportion to the distance from the point of reference
The resultant of two forces P and Q acting at an angle $$\theta $$, is
A. $${{\text{P}}^2} + {{\text{Q}}^2} + 2{\text{P}}\sin \theta $$
B. $${{\text{P}}^2} + {{\text{Q}}^2} + 2{\text{PQ}}\cos \theta $$
C. $${{\text{P}}^2} + {{\text{Q}}^2} + 2{\text{PQ}}\tan \theta $$
D. $$\sqrt {{{\text{P}}^2} + {{\text{Q}}^2} + 2{\text{PQ}}\cos \theta } $$
E. $$\sqrt {{{\text{P}}^2} + {{\text{Q}}^2} + 2{\text{PQ}}\sin \theta } $$
yes its 2/5 Mr2
Its 2/5 mr2