For the given uniform square lamina `ABCD`, where centre is `O`. Its moment of inertia about an axis `AD` is equal to how many times its moment of inertia about an axis `EF`? `1 sqrt(2) I_(AC)=I_(EF) " " 2. I_(AD)=3I_(EF)` `3.I_(AC)=4I_(EF). " " 4. I_(AC)=sqrt(2)I_(EF)`

For the given uniform square lamina `ABCD`, where centre is `O`. Its m

1.	For the given uniform square lamina `ABCD`, where centre is `O`. Its moment of inertia about an axis `AD` is equal to how many times its moment of inertia about an axis `EF`? `1 sqrt(2) I_(AC)=I_(EF) " " 2. I_(AD)=3I_(EF)` `3.I_(AC)=4I_(EF). " " 4. I_(AC)=sqrt(2)I_(EF)`
Answer» `I_(EF)=I_(GH)` (due to symmetry) `I_(AC)=I_(BD)` (due to symmetry) `I_(AC)+I_(BD)=I_(0)` `rArr2I_(AC)=I_(0).....(1)` and `I_(EF)+I_(GH)=I_(0)` `rArr2I_(EF)=I_(0)...(2)` From eq(1) and (2), we get `I_(AC)=I_(EF)` `:. I_(AD)=I_(EF)+(md^(2))/4=(md^(2))/12+(md^(2))/4` `I_(AD)=(md^(2))/3=4I_(EF)`

Discussion

No Comment Found

Related InterviewSolutions

A disc of moment of inertia `4kgm^2` is spinning freely at `3rads^(-1)`. A second disc of moment of inertia `2kgm^2` slides down the spindle and they rotate together. (a) What is the angular velocity of the combination ? (b) What is the change in kinetic energy of the system?
A uniform rod of mass `m` is supported on two rollers each of mass `m//2` and radius `r` and rolls down the inclined rough plane as shown in the figure. Assuming no slipping at any contanct and treating the rollers as uniform solid cylinders: If acceleration of rod down in the plane is `a_(R)` and acceleration of centre of mass of roller is `a_(o)` then:A. `a_(R)gta_(0)`B. `a_(R)lta_(0)`C. `a_(R)=a_(0)`D. information is insuficieng to decide
A rod leans against a stationary cylindrical body as shown in figure, and its right end sides to the right on the floor with a constant speed `v`. Choose the correct option (s) A. the angular speed `omega` is `(_Rv^(2)(2x^(2)-R^(2)))/(x^(2)(x^(2)-R^(2))^(3//2))`B. the angular acceleration `alpha` is `(Rv)/(xsqrt(x^(2)-R^(2)))`C. the angular speed `omega` is `(Rv)/(xsqrt(x^(2)-R^(2)))`D. the angular acceleration `alpha` is `(-Rv^(2)(2x^(2)-R^(2)))/(x^(2)(x^(2)-R^(2))^(3//2))`
The uniform `120 N` board shown in figure is supported by two ropes. A `400 N` weight is suspended one-fourth of the way from the left end. Choose the correct options A. `T_(1)=185N`B. `T_(2)=371N`C. `T_(2)=185N`D. `tan theta=0.257`
Three particles, each of mass `m` are placed an the points `(x_(1),y_(1),z_(1)),(x_(2),y_(2),z_(2))` and `(x_(3),y_(3),z_(3))` on the inner surface of a paraboloid of revolution obtained by rotating the parabola `x^(2)=4ay` about the `y`-axis. Neglected the mass of the paraboloid. (`y`-axis. is along the vertical (a) the moment of inertia of the system about the axis of the paraboloid is `I=4ma(y_(1)+y_(2)+y_(3))` A. the moment of inertia of the system about the axis of the paraboloid is `I=4ma(y_1+y_(2)+y_(3))`B. if potential energy at `O` is taken to be zero, the potential energy of the system is `mg(y_(1)+y_(2)+y_(3))`C. if the particle at`(x_(1),y_(1),z_(1))` slides down the smooth surface, its speed at `O` is `sqrt(2gy_(1))`D. if the parabola spins about `OY` with an angular speed, `omega`, the kinetic energy of the system will be `2ma(y_(1)+y_(2)+y_(3))omega^(2)`.
The moment of inertia of ring about an axis passing through its diameter is `I`. Then moment of inertia of that ring about an axis passing through its centre and perpendicular to its plane isA. `2I`B. `I`C. `I//2`D. `I//4`
Ratio of densities of materials of two circular discs of same mass and thickness `5:6` the ratio of their `M.I.` about natural axes isA. `5:6`B. `6:5`C. `25:26`D. `1:1`
A ring of mass `m` and radius `r` is melted and then moulded into a sphere. The moment of inertia of the sphere will beA. more than that of the ringB. less than that of the ringC. equal to that of the ringD. none of the above
Three rings, each of mass `m` and radius `r`, are so placed that they touch each other. Find the moment of inertia about the axis as shown in Fig. A. `3MR^(2)`B. `3/2 MR^(2)`C. `5MR^(2)`D. `7/2 MR^(2)`
As shown in figure from a uniform rectangular sheet a triangular sheet is removed from one edge. The shift of centre of mass is A. `4.2 cm`B. `-4.2 cm`C. `6.67 cm`D. `-6.67 cm`

For the given uniform square lamina `ABCD`, where centre is `O`. Its moment of inertia about an axis `AD` is equal to how many times its moment of inertia about an axis `EF`? `1 sqrt(2) I_(AC)=I_(EF) " " 2. I_(AD)=3I_(EF)` `3.I_(AC)=4I_(EF). " " 4. I_(AC)=sqrt(2)I_(EF)`

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment