Class 11PhysicsSystem of Particles and Rotational MotionMix Example - System of Particles and Rotational Motion
DifficultTwo rings of the same radius and mass are placed such that their centres are at a common point and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the centre and perpendicular to the plane of one of the rings is (mass of the ring $= m$,radius $= r$)
- A$1/2 \, mr^2$
- B$mr^2$
- C$3/2 \, mr^2$
- D$2 \, mr^2$
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Similar Questions
Disc $A$ and disc $B$ (with a hole) have equal mass and radius,and a string is wrapped around them as shown. An equal force $F$ is applied to the string of each body. Friction is sufficient for rolling. After time $t$,the velocity of $A$ is $v_A$ and that of $B$ is $v_B$,and their kinetic energies are $k_A$ and $k_B$ respectively. Then:
Difficult
View SolutionThree identical spherical shells,each of mass $m$ and radius $r$,are placed as shown in the figure. Consider an axis $XX'$ which touches two shells and passes through the diameter of the third shell. The moment of inertia of the system consisting of these three spherical shells about the $XX'$ axis is:
MediumAIPMT 2015
View Solution$A$ sphere of mass $M$ and radius $R$ is attached by a light rod of length $l$ to a point $P$. The sphere rolls without slipping on a circular track as shown. It is released from the horizontal position. The angular momentum of the system about $P$ when the rod becomes vertical is:
$A$ uniform cube of mass $m$ and side $a$ is placed on a frictionless horizontal surface. $A$ vertical force $F$ is applied to the edge as shown in the figure. Match the following (most appropriate choice):
$(a)$ $\frac{mg}{4} < F < \frac{mg}{2}$ $(i)$ Cube will move up $(b)$ $F > \frac{mg}{2}$ $(ii)$ Cube will not exhibit motion $(c)$ $F > mg$ $(iii)$ Cube will begin to rotate about $A$ $(d)$ $F = \frac{mg}{4}$ $(iv)$ Normal reaction effectively at $a/3$ from $A$,no motion
| $(a)$ $\frac{mg}{4} < F < \frac{mg}{2}$ | $(i)$ Cube will move up |
| $(b)$ $F > \frac{mg}{2}$ | $(ii)$ Cube will not exhibit motion |
| $(c)$ $F > mg$ | $(iii)$ Cube will begin to rotate about $A$ |
| $(d)$ $F = \frac{mg}{4}$ | $(iv)$ Normal reaction effectively at $a/3$ from $A$,no motion |
Difficult
View Solution$A$ disc and a ring of the same mass are rolling. If their kinetic energies are equal,then the ratio of their velocities will be:
Difficult
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